Introduction to CFA Level I Formula Sheet Equations and Latex Code-QUANTITATIVE ECONOMICS and FINANCIAL REPORTING

rockingdingo 2024-08-25 23:05 #CFA #CFA I #AI Courses

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In this blog, we will summarize the latex code for equations of CFA Level I exam, Formula Sheet Equations and Latex Code, and provide Chatbot as AI Assistant to facilitate your reading. You can ask question like what is "Real GDP" in the chatbox. Topics in the blog include three major parts of CFA Level I exam: QUANTITATIVE, ECONOMICS and FINANCIAL REPORTING. Detailed topics include THE TIME VALUE OF MONEY, Future Value, Present Value, Effective Annual Rate, Continuous Compounding, Ordinary Annuity, Annuity Due, Perpetuity, STATISTICAL CONCEPT AND MARKET RETURNS, Fisher Skewness, Kurtosis, Two-asset portfolio, Three-asset portfolio, Microeconomics, Simple Interest, Effective Rate, Future Value of Ordinary Annuities, Annuities Due, Present Value of Ordinary Annuities, Allocative Efficiency Condition, Average Fixed Cost; Macroeconomics Investment, Aggregate Expenditure Without Government or Foreign Sectors, Marginal Propensity to Consume MPC, Marginal Propensity Save MPS, Sum of Marginal Propensity to Save and Marginal Propensity to Consume, Autonomous Spending Multiplier, Balanced Budget Multiplier, Banks Reserve Ratio, Nominal Interest Rate, Real GDP, Real Interest Rate, Tax Multiplier, Unemployment Rate. FINANCIAL REPORTING and ANALYSIS, Basic EPS, Diluted EPS, Balance Sheet, Free Cash Flow to the Firm, Cash Flow Performance Ratio, Cash Flow To Revenue Ratio, Cash Return On Assets, Cash Return On Assets, Cash Return On Equity, Activity Ratio, Inventory Turnover, Days of Inventory On Hand (DOH), Receivables Turnover, Days of Sales Outstanding, etc. Tag: CFA,CFA I,AI Courses

1. QUANTITATIVE METHODS

THE TIME VALUE OF MONEY

Future Value

Present Value

Effective Annual Rate

Continuous Compounding

Ordinary Annuity

Annuity Due

Perpetuity

STATISTICAL CONCEPT AND MARKET RETURNS

Mean and Variance

Standard Deviation

Probability Distributions

Binomial Distribution

Poisson Distribution

Normal Gaussian Distribution

Chi-Square Test

Advanced Statistics

Sum of Random Variables

Covariance

Gamma Distribution

Fisher Skewness

Kurtosis

Two-asset portfolio

Three-asset portfolio

2. ECONOMICS

Microeconomics

Simple Interest

Effective Rate

Future Value of Ordinary Annuities

Annuities Due

Present Value of Ordinary Annuities

Allocative Efficiency Condition

Average Fixed Cost

Average Product

Average Profit

Average Revenue

Average Total Cost

Average Variable Cost

Cross-Price Elasticity of Demand

Distributive Efficiency Condition

Elasticity of Supply

Factor of Production Hiring Rule

Marginal Revenue Product

Gini Coefficient

Marginal Cost

Marginal Product of Labor

Marginal Revenue

Marginal Factor Cost MFC

Marginal Revenue Product of Labor MRPL

Optimal Combination of Resources Condition

Optimal Consumption Rule

Price Elasticity of Demand

Price for a Competitive Firm

Production Efficiency Condition

Profit

Profit-Maximizing Output Level

Slope of the Total Product Curve

Socially Optimal Level of Output

Total Costs

Macroeconomics

Investment

Aggregate Expenditure Without Government or Foreign Sectors

Marginal Propensity to Consume MPC

Marginal Propensity Save MPS

Sum of Marginal Propensity to Save and Marginal Propensity to Consume

Autonomous Spending Multiplier

Balanced Budget Multiplier

Banks Reserve Ratio

Budget Deficit

Financial Account Balance

Consumer Price Index CPI

Consumption Function

Current-Account Balance

Equality of Leakages and Injections

Equation of Exchange

Gross Domestic Product GDP

Gross Domestic Product Deflator

Inflation Between Two Years

Merchandise Trade Balance

Nominal Interest Rate

Real GDP

Real Interest Rate

Tax Multiplier

Unemployment Rate

3. FINANCIAL REPORTING & ANALYSIS

Basic EPS

Diluted EPS

Balance Sheet

Free Cash Flow to the Firm

Cash Flow Performance Ratio

Cash Flow To Revenue Ratio

Cash Return On Assets

Cash Return On Assets

Cash Return On Equity

Cash To Income

Cash flow Per Share

Debt Coverage Ratio

Interest coverage ratio

Reinvestment Coverage Ratio

Debt Payment Coverage Ratio

Activity Ratio

Inventory Turnover

Days of Inventory On Hand (DOH)

Receivables Turnover

Days of Sales Outstanding

THE TIME VALUE OF MONEY

Future Value
Future Value
Equation

$$FV=PV(1+r)^n$$

Latex Code
```
            FV=PV(1+r)^n
        
```
Explanation

Latex code for Future Value Equation
- $$FV$$: Future Value of Money
- $$PV$$: Present Value of Money
- $$r$$: Interest rate per period
- $$n$$: Period
Related Documents
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Present Value
Present Value
Equation

$$PV=\frac{FV}{(1+r)^n}$$

Latex Code
```
            PV=\frac{FV}{(1+r)^n}
        
```
Explanation

Latex code for Present Value of Money Equation
- $$FV$$: Future Value of Money
- $$PV$$: Present Value of Money
- $$r$$: Interest rate per period
- $$n$$: Period
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Effective Annual Rate
Effective Annual Rate
Equation

$$\text{EAR}=(1+\frac{r}{m})^{m}-1$$

Latex Code
```
             \text{EAR}=(1+\frac{r}{m})^{m}-1
        
```
Explanation

Latex code for Effective Annual Rate
- $$r$$: Interest rate per period
- $$n$$: Period
- $$m$$: Compounding frequency is m times per year
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Continuous Compounding
Continuous Compounding
Equation

$$FV=PV \times e^{r_{c} \times n}$$
$$PV=FV \times e^{-r_{c} \times n}$$

Latex Code
```
             FV=PV \times e^{r_{c} \times n} \\
             PV=FV \times e^{-r_{c} \times n}
        
```
Explanation

Latex code for Continuous Compounding
- $$r_{c}$$: Continuously compounded rate of return
- $$FV$$: Future Value
- $$PV$$: Present Value
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Ordinary Annuity
Ordinary Annuity
Equation

$$FV=\frac{A}{r}[(1+r)^{n}-1]$$
$$PV=\frac{A}{r}[1-\frac{1}{(1+r)^{n}}]$$

Latex Code
```
             FV=\frac{A}{r}[(1+r)^{n}-1] \\
             PV=\frac{A}{r}[1-\frac{1}{(1+r)^{n}}]
        
```
Explanation

Latex code for Ordinary Annuity
- $$A$$: Annuity amount per year
- $$r$$: Interest Rate
- $$FV$$: Future Value
- $$PV$$: Present Value
Related Documents
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Annuity Due
Annuity Due
Equation

$$FV=\frac{A}{r}[(1+r)^{n}-1](1+r)$$
$$PV=\frac{A}{r}[1-\frac{1}{(1+r)^{n}}](1+r)$$

Latex Code
```
             FV=\frac{A}{r}[(1+r)^{n}-1](1+r) \\
             PV=\frac{A}{r}[1-\frac{1}{(1+r)^{n}}](1+r)
        
```
Explanation

Latex code for Annuity Due
- $$A$$: Annuity amount per year
- $$r$$: Interest Rate
- $$FV$$: Future Value
- $$PV$$: Present Value
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THE TIME VALUE OF MONEY

Perpetuity
Perpetuity
Equation

$$PV=\frac{A}{r}$$
$$PV=\frac{A}{r}(1+r)$$

Latex Code
```
             PV=\frac{A}{r} \\
             PV=\frac{A}{r}(1+r)
        
```
Explanation

Latex code for Annuity Due
- $$PV=\frac{A}{r}$$: First cash flow occurs one period from now
- $$PV=\frac{A}{r}(1+r)$$: First cash flow occurs immediately
- $$A$$: Annuity amount per year
- $$r$$: Interest Rate
- $$FV$$: Future Value
- $$PV$$: Present Value
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STATISTICAL CONCEPT AND MARKET RETURNS

Mean and Variance

Equation

$$\text{Mean Discrete}\ \mu=E(X)=\sum P_{i}x_{i}$$
$$\text{Mean Continuous}\ \mu=\int xf(x) dx$$
$$\text{Variance Discrete}\ \sigma^{2}=V(X)=E[(X-\mu)^2]=\sum P_{i}(x_{i} -\mu)^2$$
$$\text{Variance Continuous}\ \sigma^{2}=V(X)=E[(X-\mu)^2]=\int (x-\mu)^{2}f(x) dx$$

Latex Code
```
        \text{Mean Discrete}\ \mu=E(X)=\sum P_{i}x_{i} \\\text{Mean Continuous}\ \mu=\int xf(x) dx \\\text{Variance Discrete}\ \sigma^{2}=V(X)=E[(X-\mu)^2]=\sum P_{i}(x_{i} -\mu)^2 \\\text{Variance Continuous}\ \sigma^{2}=V(X)=E[(X-\mu)^2]=\int (x-\mu)^{2}f(x) dx
        
```
Explanation

X denotes a random variable which has a distribution f(x) over some subset x of the real numbers. If the distribution f(x) is discrete, the probability of f(x=X)=xi is is Pi. And the mean \mu equals to the sum of probability Pi multiplies the random variable value x. . When the distribution is continuous f(x), the probability that X lies in the interval, and the f(x) denotes density function. The variance(squared value of standard deviation \sigma) measure how far the subset X is from the mean value \mu, is it a flat distribution or shallow distribution. And the definition of variance is the expectation E(X) of the squared distance between each data point X and its mean \mu.
Standard Deviation

Equation

$$\sigma=\sqrt{V(X)}=\sqrt{\sum_{i} P_{i}(x_{i} - \mu)^2}=\sqrt{\frac{\sum_{i} (x_{i} - \mu)^2}{n}}$$
$$\sigma=\sqrt{V(X)}=\sqrt{\int (x-\mu)^{2}f(x) dx}$$

Latex Code
```
        \sigma=\sqrt{V(X)}=\sqrt{\sum_{i} P_{i}(x_{i} - \mu)^2}=\sqrt{\frac{\sum_{i} (x_{i} - \mu)^2}{n}} \\ \sigma=\sqrt{V(X)}=\sqrt{\int (x-\mu)^{2}f(x) dx}
        
```
Explanation

Standard Deviation \sigma equals to the squared root of Variance \sigma^{2} of a dataset X.

Probability Distributions

Binomial Distribution

Equation
$$X \sim B(n,p)$$
$$f(x)=\begin{pmatrix}n\\ x\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p$$
$$\text{Binominal Mean}\ \mu=np$$
$$\text{Binominal Variance}\ \sigma^2=npq$$

Latex Code
```
        X \sim B(n,p) \\f(x)=\begin{pmatrix}n\\ x\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\text{Binominal Mean}\ \mu=np\\\text{Binominal Variance}\ \sigma^2=npq
        
```
Explanation

The binomial distribution measures in total n independent trials, the probability that x trials in total n trials are positive (like the getting positive of flipping a coin). In this formulation, f(x) denotes the probability that x positive trials are observed in n independent trials. p denote the probability that positive is observed in each single trial. q denotes the negative is observed, which equals to 1-p.
Poisson Distribution

Equation
$$X \sim \pi(\mu)$$
$$f(x)=\frac{\mu^{x}}{x!}e^{-\mu}$$
$$\text{Poisson Mean } \mu$$
$$\text{Poisson Variance }\sigma^2=\mu$$

Latex Code
```
        X \sim \pi(\mu) \\f(x)=\frac{\mu^{x}}{x!}e^{-\mu}\\ \text{Poisson Mean} \mu \\  \text{Poisson Variance}\sigma^2=\mu
        
```
Explanation

\mu equals to the probability that an event occurs in a unit time period.
Normal Gaussian Distribution

Equation

$$X \sim \mathcal{N}(\mu,\sigma^2)$$
$$f(x)=\frac{1}{\sigma\sqrt{2\pi}}\exp{[-\frac{(x-\mu)^{2}}{2\sigma^{2}}]}$$

Latex Code
```
        X \sim \mathcal{N}(\mu,\sigma^2) \\ f(x)=\frac{1}{\sigma\sqrt{2\pi}}\exp{[-\frac{(x-\mu)^{2}}{2\sigma^{2}}]}
        
```
Explanation

X denotes the random variable which follows the normal distribution. \mu denotes the mean value and \sigma denotes the standard deviation.
Chi-Square Test

Equation
$$\chi ^{2}=\sum \frac{(A-E)^2}{E}$$
$$=\sum^{K}_{1}\frac{(A_{i}-E_{i})^2}{E_{i}}=\sum^{K}_{1}\frac{(A_{i}-np_{i})^2}{np_{i}}$$

Latex Code
```
        \chi ^{2}=\sum \frac{(A-E)^2}{E}\\=\sum^{K}_{1}\frac{(A_{i}-E_{i})^2}{E_{i}}=\sum^{K}_{1}\frac{(A_{i}-np_{i})^2}{np_{i}}
        
```
Explanation

Chi-Square Test measure how close and an actual observation of distribution A are correlated to the assumed theoretical distribution E. The dataset X are splitted into K different buckets and the statistics of Chi-Square Test is calculated as above.

3. Advanced Statistics

Sum of Random Variables

Equation
$$W=aX+bY$$
$$E(W)=aE(X)+bE(Y)$$
$$\text{Var}(W)=a^{2}\text{Var}(X) + b^{2}\text{Var}(Y), \text{X and Y independent}$$

Latex Code
```
        W=aX+bY \\ E(W)=aE(X)+bE(Y) \\ \text{Var}(W)=a^{2}\text{Var}(X) + b^{2}\text{Var}(Y), \text{X and Y independent}
        
```
Explanation

E(X) and E(Y) denote the mean of random variable X and Y, Var(X) and Var(Y) denote the variance of random variable X and Y. W is the weighted sum of two random variables.
Covariance

Equation
$$\text{Cov}(X,Y)=E[(X-E(X))(Y-E(Y))]$$
$$=E(XY)-2E(X)E(Y)+E(X)E(Y)$$
$$=E(XY)-E(X)E(Y)$$

Latex Code
```
        \text{Cov}(X,Y)=E[(X-E(X))(Y-E(Y))]\\=E(XY)-2E(X)E(Y)+E(X)E(Y)\\=E(XY)-E(X)E(Y)
        
```
Explanation

Covariance measures the total variation of two random variables X and Y from their expected values E(X) and E(Y). The definition of covariance is E[(X-E(X))(Y-E(Y))].
Gamma Distribution
Math,Statistics
Equation
$$\Gamma \left( a \right) = \int\limits_0^\infty {s^{a - 1} } e^{ - s} ds$$
$$P(x) = \frac{x^{\alpha-1} e^{-frac{x}{\theta}}}{\Gamma(\alpha) \theta^{\alpha}}$$
$$\mu = \alpha \theta$$
$$\sigma^{2} = \alpha \theta^{2}$$
$$\gamma_{1} = \frac{2}{\sqrt{\alpha}}$$
$$\gamma_{2} = \frac{6}{\alpha}$$

Latex Code
```
            \Gamma \left( a \right) = \int\limits_0^\infty {s^{a - 1} } e^{ - s} ds \\
            P(x) = \frac{x^{\alpha-1} e^{-frac{x}{\theta}}}{\Gamma(\alpha) \theta^{\alpha}} \\
            \mu = \alpha \theta \\
            \sigma^{2} = \alpha \theta^{2} \\
            \gamma_{1} = \frac{2}{\sqrt{\alpha}} \\
            \gamma_{2} = \frac{6}{\alpha}
        
```
Explanation

Latex code for Gamma Distribution. A gamma distribution is a general type of statistical distribution that is related to the beta distribution and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. Gamma distributions have two free parameters, labeled alpha and theta. We now let W denote the waiting time until the a-th event occurs and find the distribution of W. We could represent the situation as follows:
- $$\Gamma(a)$$ : Gamma function of a
- $$\alpha$$: Gamma function parameter
- $$P(x) = \frac{x^{\alpha-1} e^{-frac{x}{\theta}}}{\Gamma(\alpha) \theta^{\alpha}}$$: PDF of gamma distributed random variable X.
- $$\mu = \alpha \theta$$: Mean of Gamma Distribution
- $$\sigma^{2} = \alpha \theta^{2}$$: Variance of Gamma Distribution
- $$\gamma_{1} = \frac{2}{\sqrt{\alpha}}$$: Skewness of Gamma Distribution
- $$\gamma_{2} = \frac{6}{\alpha}$$: Kurtosis of Gamma Distribution
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- Gamma Distribution
- 15.4 - Gamma Distributions
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Fisher Skewness
Math,Statistics
Equation
Skewness measures $$ g_{1} = \frac{\sum_{i=1}^{n}{(x_{i} - \bar{x})^{3}}/n} {s^{3}}$$ The adjusted Fisher-Pearson skewness coefficient is: $$G_{1} = \frac{\sqrt{n(n-1)}}{n-2} \frac{\sum_{i=1}^{n}{(x_{i} - \bar{x})}/n} {s^{3}}$$

Latex Code
```
            g_{1} = \frac{\sum_{i=1}^{n}{(x_{i} - \bar{x})^{3}}/n} {s^{3}} \\
            G_{1} = \frac{\sqrt{n(n-1)}}{n-2} \frac{\sum_{i=1}^{n}{(x_{i} - \bar{x})}/n} {s^{3}}
        
```
Explanation

Latex code for Fisher Skewness. Skewness measures the lack of symmetry in a variable. The formula for the Fisher-Pearson skewness coefficient is: The formula for the Fisher-Pearson skewness coefficient is:
- Fisher-Pearson skewness coefficient: $$g_{1} = \frac{\sum_{i=1}^{n}{(x_{i} - \bar{x})^{3}}/n} {s^{3}}$$
- Adjusted Fisher-Pearson skewness coefficient: $$G_{1} = \frac{\sqrt{n(n-1)}}{n-2} \frac{\sum_{i=1}^{n}{(x_{i} - \bar{x})}/n} {s^{3}}$$
Related Documents
- SKEWNESS
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Kurtosis
Math,Statistics
Equation
$$\mbox{kurtosis} = \frac{\sum_{i=1}^{N}(Y_{i} - \bar{Y})^{4}/N} {s^{4}}$$
Latex Code
```
            \mbox{kurtosis} = \frac{\sum_{i=1}^{N}(Y_{i} - \bar{Y})^{4}/N} {s^{4}}
        
```
Explanation

For univariate data Y1, Y2, ..., YN, the formula for kurtosis is as below, Note that in computing the kurtosis, the standard deviation is computed using N in the denominator rather than N - 1.
- $$\bar{Y}$$: Mean
- $$s$$: Standard deviation
- $$N$$: Number of data points
Related Documents
- NIST HANDBOOK Kurtosis
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Two-asset portfolio
Math,Statistics
Equation
$$E(R_{p})=w_{1}E(R_{1}) + w_{2} E(R_{2})$$
$$\sigma^{2}(R_{p})=w^{2}_{1}\sigma^{2}(R_{1})+w^{2}_{2}\sigma^{2}(R_{2}) + 2w_{1}w_{2}Cov(R_{1},R_{2})$$

Latex Code
```
            E(R_{p})=w_{1}E(R_{1}) + w_{2} E(R_{2}) \\
            \sigma^{2}(R_{p})=w^{2}_{1}\sigma^{2}(R_{1})+w^{2}_{2}\sigma^{2}(R_{2}) + 2w_{1}w_{2}Cov(R_{1},R_{2})
        
```
Explanation

Explanation for Two-asset portfolio:
- $$E(R_{p})$$: Portfolio return
- $$\sigma^{2}(R_{p})$$: Portfolio variance
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Three-asset portfolio
Math,Statistics
Equation
$$E(R_{p})=w_{1}E(R_{1}) + w_{2} E(R_{2}) +w_{3} E(R_{3}) $$
$$\sigma^{2}(R_{p})=w^{2}_{1}\sigma^{2}(R_{1})+w^{2}_{2}\sigma^{2}(R_{2}) + w^{2}_{3}\sigma^{2}(R_{3}) + 2w_{1}w_{2}Cov(R_{1},R_{2}) + 2w_{1}w_{3}Cov(R_{1},R_{3}) + 2w_{2}w_{3}Cov(R_{2},R_{3})$$
Latex Code
```
            E(R_{p})=w_{1}E(R_{1}) + w_{2} E(R_{2}) +w_{3} E(R_{3}) \\
            \sigma^{2}(R_{p})=w^{2}_{1}\sigma^{2}(R_{1})+w^{2}_{2}\sigma^{2}(R_{2}) + w^{2}_{3}\sigma^{2}(R_{3}) + 2w_{1}w_{2}Cov(R_{1},R_{2}) + 2w_{1}w_{3}Cov(R_{1},R_{3}) + 2w_{2}w_{3}Cov(R_{2},R_{3})
        
```
Explanation

Explanation for Three-asset portfolio:
- $$E(R_{p})$$: Portfolio return
- $$\sigma^{2}(R_{p})$$: Portfolio variance
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2. Economics

MicroEconomics

1. Microeconomics

Simple Interest
Economics
Equation

$$I=Prt \\ A=P(1+rt)$$

Latex Code
```
            I=Prt \\
            A=P(1+rt)
        
```
Explanation

Latex code for the Simple Interest. I will briefly introduce the notations in this formulation.
- $$I$$: Interest Earned
- $$P$$: Principal/Present Value
- $$r$$: Annual Rate
- $$t$$: Time (years)
- $$A$$: Future Value/Maturity Value
Related Documents
- Investopedia Simple Interest
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Compound Interest
Economics
Equation

$$A = P(1+\frac{r}{m})^{mt}$$
$$A = Pe^{rt}$$

Latex Code
```
            A = P(1+\frac{r}{m})^{mt} \\
            A = Pe^{rt}
        
```
Explanation

Latex code for the Compound Interest. I will briefly introduce the notations in this formulation.
- $$A$$: Future Value/Maturity Value
- $$P$$: Principal/Present Value
- $$A$$: Annual Rate (decimal)
- $$m$$: Number of Compounding Periods per Year
- $$t$$: Time (years)
- $$A = Pe^{rt}$$: Loan/investment is compounded continuously
Related Documents
- Compound Interest Calculator
- Investopedia Compound Interest
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Effective Rate
Economics
Equation

$$r_{e} = (1 + \frac{r}{m})^{m} - 1$$
$$r_{e} = e^{r} - 1$$

Latex Code
```
            r_{e} = (1 + \frac{r}{m})^{m} - 1 \\
            r_{e} = e^{r} - 1
        
```
Explanation

Latex code for the Effective Rate. I will briefly introduce the notations in this formulation.
- $r_{e}$ : Effective Rate
- $r_{e} = (1 + \frac{r}{m})^{m} - 1$ : Compute the effective rate if your loan/investment is compounded m times per year.
- $r_{e} = e^{r} - 1$ : Compute the effective rate if your loan/investment is compounded continuously.
Related Documents
- Investopedia Effective Rate
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Future Value of Ordinary Annuities
Economics
Equation

$$S = R \times \frac{(1+i)^n - 1}{i}$$
$$R = S \times \frac{i}{(1+i)^n - 1}$$

Latex Code
```
            S = R \times \frac{(1+i)^n - 1}{i} \\
            R = S \times \frac{i}{(1+i)^n - 1}
        
```
Explanation

Latex code for the Future Value of Ordinary Annuities. The payment/deposit is at the END of the period. I will briefly introduce the notations in this formulation.
- $$S$$: Future Value/Total amount accrued
- $$R$$: Payment/Deposit made in each period
- $$i$$: Rate per period
- $$n$$: Total number of times compounded
Related Documents
- Ordinary Annuity
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Annuities Due
Economics
Equation

$$S = R \times \frac{(1+i)^(n+1) - 1}{i} - R$$

Latex Code
```
            S = R \times \frac{(1+i)^(n+1) - 1}{i} - R
        
```
Explanation

Latex code for the Future Value of Annuities Due. I will briefly introduce the notations in this formulation. The payment/deposit is at the BEGINNING of the period
- $$S$$: Future Value/Total amount accrued
- $$R$$: Payment/Deposit made in each period
- $$i$$: Rate per period
- $$n$$: Total number of times compounded
Related Documents
- Ordinary Annuity
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Present Value of Ordinary Annuities
Economics
Equation

$$P = R \frac{1 - (1+r)^{-n}}{i}$$
$$R = P \frac{i}{1 - (1+r)^{-n}}$$

Latex Code
```
            P = R \frac{1 - (1+r)^{-n}}{i} \\
            R = P \frac{i}{1 - (1+r)^{-n}}
        
```
Explanation

Latex code for the Present Value of Ordinary Annuities. I will briefly introduce the notations in this formulation. The payment is made at the END of the period.
- $$S$$: Future Value/Total amount accrued
- $$R$$: Payment/Deposit made in each period
- $$i$$: Rate per period
- $$n$$: Total number of times compounded
Related Documents
- Ordinary Annuity
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Allocative Efficiency Condition
Economics,Microeconomics
Equation

$$P = MC$$
$$\text{Marginal Social Benefit (MSB)} = \text{Marginal Social Cost (MSC)}$$

Latex Code
```
            P = MC \\
            \text{Marginal Social Benefit (MSB)} = \text{Marginal Social Cost (MSC)}
        
```
Explanation

Latex code for the Allocative Efficiency Condition. I will briefly introduce the notations in this formulation. Allocative efficiency occurs when consumer demand is completely met by supply. In other words, businesses are providing the exact supply that consumers want.
- $$MSB$$: Marginal Social Benefit
- $$MSC$$: Marginal Social Cost
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- Allocative Efficiency: Definition, Example Productive Efficiency
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Average Fixed Cost
Economics,Microeconomics
Equation

$$AFC = \frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}$$

Latex Code
```
            AFC = \frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}
        
```
Explanation

Latex code for the Allocative Average Fixed Cost. I will briefly introduce the notations in this formulation.
- $TFC$ : Total Fixed Cost
- $Q$ : Quantity of Output
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Average Product
Economics,Microeconomics
Equation
$$\text{AP} = \frac{\text{Total Product}}{\text{Quantity of Input}}$$

Latex Code
```
            \text{AP} = \frac{\text{Total Product}}{\text{Quantity of Input}}
        
```
Explanation

Latex code for the Average Product. I will briefly introduce the notations in this formulation.
- $$AP$$: Average Product
- $$TP$$: Total Product
- $$QI$$: Quantity of Input
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Average Profit
Economics,Microeconomics
Equation
$$\text{Average Profit} = \frac{\text{Total Profit}}{\text{Quantity}}$$

Latex Code
```
            \text{Average Profit} = \frac{\text{Total Profit}}{\text{Quantity}}
        
```
Explanation

Latex code for the Average Profit. I will briefly introduce the notations in this formulation.
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Average Revenue
Economics,Microeconomics
Equation

$$\text{Average Revenue} = \frac{\text{Total Revenue}}{\text{Quantity}}$$

Latex Code
```
            \text{Average Revenue} = \frac{\text{Total Revenue}}{\text{Quantity}}
        
```
Explanation

Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.
Related Documents
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Average Total Cost
Economics,Microeconomics
Equation

$\text{Average Revenue} = \frac{\text{Total Revenue}}{\text{Quantity}}$

Latex Code
```
            \text{Average Total Cost(ATC)} = \frac{\text{Total Cost (TC)}}{\text{Quantity of Output (Q)}}
        
```
Explanation

Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.
- $ATC$ : Average Total Cost
- $TC$ : Total Cost
- $Q$ : Quantity of Output
Related Documents
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Average Variable Cost
Economics,Microeconomics
Equation

$\text{Average Revenue} = \frac{\text{Total Revenue}}{\text{Quantity}}$

Latex Code
```
            \text{Average Variable Cost(AVC)} = \frac{\text{Total Variable Cost (TVC)}}{\text{Quantity of Output (Q)}}
        
```
Explanation

Latex code for the Average Variable Cost. I will briefly introduce the notations in this formulation.
- $AVC$ : Average Variable Cost
- $TC$ : Total Variable Cost
- $Q$ : Quantity of Output
Related Documents
Related Videos
Cross-Price Elasticity of Demand
Economics,Microeconomics
Equation

$\text{Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded of Good X}}{\text{Percentage Change in Price of Good Y}}$

Latex Code
```
            \text{Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded of Good X}}{\text{Percentage Change in Price of Good Y}}
        
```
Explanation

Latex code for Cross-Price Elasticity of Demand. I will briefly introduce the notations in this formulation.
Related Documents
Related Videos
Distributive Efficiency Condition
Economics,Microeconomics
Equation

$\frac{MU_{F}}{P_{F}} = \frac{MU_{C}}{P_{C}}$

Latex Code
```
            \frac{MU_{F}}{P_{F}} = \frac{MU_{C}}{P_{C}}
        
```
Explanation

Latex code for Distributive Efficiency Condition. I will briefly introduce the notations in this formulation. Distributive efficiency is concerned with an equitable distribution of resources because of the law of diminishing marginal returns. The Law of diminishing marginal returns states that as consumption of a good increase we tend to get diminishing marginal utility.
- $MU_{F}$ : Marginal Utility of F
- $P_{F}$ : Product of F
- $MU_{C}$ : Marginal Utility of C
- $P_{C}$ : Product of C
Related Documents
- Distributive Efficiency Definition
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Elasticity of Supply
Economics,Microeconomics
Equation

$\text{Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded of Good X}}{\text{Percentage Change in Price of Good Y}}$

Latex Code
```
            \text{Elasticity of Supply} = \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}
        
```
Explanation

Latex code for Elasticity of Supply. I will briefly introduce the notations in this formulation.
Related Documents
Related Videos
Factor of Production Hiring Rule
Economics,Microeconomics
Equation

$\text{MRP} = \text{MFC}$

Latex Code
```
            \text{MRP} = \text{MFC}
        
```
Explanation

Latex code for Factor of Production Hiring Rule. I will briefly introduce the notations in this formulation.
- $MRP$ : Marginal revenue product
- $MFC$ : Marginal factor cost (MFC)
Related Documents
- The Demand for Labor
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Marginal Revenue Product
Economics,Microeconomics
Equation

$\text{MRP} = \text{MP} \times \text{MR}$

Latex Code
```
            \text{MRP} = \text{MP} \times \text{MR}
        
```
Explanation

Latex code for Marginal Revenue Product. The amount that an additional unit of a factor adds to a firm's total revenue during a period is called the marginal revenue product (MRP) of the factor. An additional unit of a factor of production adds to a firm’s revenue in a two-step process: first, it increases the firm's output. Second, the increased output increases the firm’s total revenue. We find marginal revenue product by multiplying the marginal product (MP) of the factor by the marginal revenue (MR). I will briefly introduce the notations in this formulation.
- $MP$ : Marginal Product(MP)
- $MR$ : Marginal Revenue(MR)
Related Documents
- The Demand for Labor
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Gini Coefficient
Economics,Microeconomics
Equation

$G = \frac{S_{A}}{S_{B}} \\ G = 1 - \sum^{n}_{i=1} P_{i} \times (2 Q_{i} - W_{i}) \\ Q_{i} = \sum^{i}_{k = 1} W_{k}$

Latex Code
```
            G = \frac{S_{A}}{S_{B}} \\
            G = 1 - \sum^{n}_{i=1} P_{i} \times (2 Q_{i} - W_{i}) \\
            Q_{i} = \sum^{i}_{k = 1} W_{k} 
        
```
Explanation

Latex code for Gini Coefficient. The Gini coefficient (Gini index or Gini ratio) is a statistical measure of economic inequality in a population. The coefficient measures the dispersion of income or distribution of wealth among the members of a population.
- $S_{A}$ : Area between Line of Perfect Equality and Lorenz Curve.
- $S_{B}$ : Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income).
- $W_{i}$ : The ratio of i-th group's income/total income
- $Q_{i}$ : The ratio of cumulative i-th group's income(increasing order)/total income
- $P_{i}$ : The ratio of i-th group's population(P)/total population(P)
Related Documents
- Corporate Finance Institute Gini-coefficient
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Marginal Cost
Economics,Microeconomics
Equation

$\text{MC} = \frac{\Delta \text{TC}}{\Delta \text{Q}} = \frac{\Delta \text{TVC}}{\Delta \text{Q}}$

Latex Code
```
            \text{MC} = \frac{\Delta \text{TC}}{\Delta \text{Q}} = \frac{\Delta \text{TVC}}{\Delta \text{Q}}
        
```
Explanation

Latex code for Marginal Cost.
- $TC$ : Total Cost(TC)
- $\Delta \text{TC}$ : Change in Total Cost(TC)
- $Q$ : Quantity
- $\Delta \text{Q}$ : Change in Quantity
Related Documents
- Investopedia Marginal Cost
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Marginal Product of Labor
Economics,Microeconomics
Equation

$\text{MPL} = \frac{\Delta \text{TC}}{\Delta \text{L}}$

Latex Code
```
            \text{MPL} = \frac{\Delta \text{TP}}{\Delta \text{L}}
        
```
Explanation

Latex code for Marginal Product of Labor.
- $MPL$ : Marginal Product of Labor
- $\Delta \text{TP}$ : Change in Total Product(TP)
- $\Delta \text{L}$ : Change in Labor(L)
Related Documents
- How Is the Marginal Product of Labor Determined
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Marginal Revenue
Economics,Microeconomics
Equation

$\text{MR} = \frac{\Delta \text{TR}}{\Delta \text{Q}}$

Latex Code
```
            \text{MR} = \frac{\Delta \text{TR}}{\Delta \text{Q}}
        
```
Explanation

Latex code for Marginal Revenue.
- $MR$ : Marginal Revenue
- $\Delta \text{TR}$ : Change in Total Revenue(TR)
- $\Delta \text{Q}$ : Change in Quantity(Q)
Related Documents
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Marginal Factor Cost MFC
Economics,Microeconomics
Equation

$\text{MRP}_{L} = \text{MP}_{L} \times \text{P}$

Latex Code
```
            \text{MFC} = \frac{\Delta \text{TC}}{\Delta \text{f}}
        
```
Explanation

Latex code for Marginal Factor Cost MFC. Marginal factor cost (MFC) is the change in total cost (\Delta \text{TC}}) divided by the change in the quantity of the factor:
- $\text{MFC}$ : Marginal Factor Cost
- $\Delta \text{TC}$ : Change in total cost
- $\Delta \text{f}$ : Change in the quantity of the factor
Related Documents
- How Is the Marginal Product of Labor Determined
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Marginal Revenue Product of Labor MRPL
Economics,Microeconomics
Equation

$\text{MRP}_{L} = \text{MP}_{L} \times \text{P}$

Latex Code
```
            \text{MRP}_{L} = \text{MP}_{L} \times \text{P}
        
```
Explanation

Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.
- $\text{MRP}_{L}$ : Marginal Revenue Product of Labor
- $\text{MP}_{L}$ : Marginal Product of Labor
- $P$ : Price
Related Documents
- How Is the Marginal Product of Labor Determined
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Optimal Combination of Resources Condition
Economics,Microeconomics
Equation

$\text{MRP}_{L} = \text{MP}_{L} \times \text{P}$

Latex Code
```
            \text{MRP}_{L} = \text{MP}_{L} \times \text{P}
        
```
Explanation

Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.
- $\text{MRP}_{L}$ : Marginal Revenue Product of Labor
- $\text{MP}_{L}$ : Marginal Product of Labor
- $P$ : Price
Related Documents
- How Is the Marginal Product of Labor Determined
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Optimal Consumption Rule
Economics,Microeconomics
Equation

$\frac{MU_{x}}{P_{x}} = \frac{MU_{Y}}{P_{Y}}$

Latex Code
```
            \frac{MU_{x}}{P_{x}} = \frac{MU_{Y}}{P_{Y}}
        
```
Explanation

Latex code for Optimal Consumption Rule.
- $MU$ : Marginal utility (MU)
- $P$ : Price
Related Documents
- How Is the Marginal Product of Labor Determined
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Price Elasticity of Demand
Economics,Microeconomics
Equation

$\text{Price Elasticity of Demand} = \frac{% \Delta Q_{d}}{% \Delta P} = \frac{\frac{\Delta Q_{d}}{Q}}{\frac{\Delta P}{P}}$

Latex Code
```
            \text{Price Elasticity of Demand} = \frac{% \Delta Q_{d}}{% \Delta P} = \frac{\frac{\Delta Q_{d}}{Q}}{\frac{\Delta P}{P}}
        
```
Explanation

Latex code for Price Elasticity of Demand. Price Elasticity of Demand= Percentage change in quantity demanded / Percentage change in Price
- $% \Delta Q_{d}$ : Percentage change in quantity demanded
- $% \Delta P$ : Percentage change in Price
Related Documents
- Investopedia Price Elasticity of Demand
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Price for a Competitive Firm
Economics,Microeconomics
Equation

$P=MR$

Latex Code
```
            P = MR
        
```
Explanation

Latex code for Price for a Competitive Firm.
- $MR$ : Marginal revenue (MR)
- $P$ : Price
Related Documents
- Investopedia Price Elasticity of Demand
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Production Efficiency Condition
Economics,Microeconomics
Equation

$\frac{w}{r} = \frac{MP_{L}}{MP_{K}}$

Latex Code
```
            \frac{w}{r} = \frac{MP_{L}}{MP_{K}}
        
```
Explanation

Latex code for Price for a Competitive Firm.
- $MP_{L}$ : Marginal Product Label
Related Documents
- Production Efficiency
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Profit
Economics,Microeconomics
Equation

$\text{Profit} = \text{TR} - \text{TC}$

Latex Code
```
            \text{Profit} = \text{TR} - \text{TC}
        
```
Explanation

Latex code for Price for a Competitive Firm.
- $\text{TR}$ : Total Revenue
- $\text{TC}$ : Total Cost
Related Documents
- Profit
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Profit-Maximizing Output Level
Economics,Microeconomics
Equation

$MR = MC$

Latex Code
```
            MR = MC
        
```
Explanation

Latex code for Profit-Maximizing Output Level.
- $\text{MR}$ : Marginal Revenue
- $\text{MC}$ : Marginal Cost
Related Documents
- Profit
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Slope of the Total Product Curve
Economics,Microeconomics
Equation

$\text{Marginal Product} = \frac{\text{Rise}}{\text{Run}} = \frac{\text{Change in Total Product}}{\text{Change in the Number of Units of an Input}}$

Latex Code
```
            \text{Marginal Product} = \frac{\Delta P}{\Delta L} = \frac{\text{Rise}}{\text{Run}} = \frac{\text{Change in Total Product}}{\text{Change in the Number of Units of an Input}}
        
```
Explanation

Latex code for Slope of the Total Product Curve.
- $\Delta Q$ : Change in Total Product
- $\text{TPC}$ : Total Product Curve
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- 8-1-production-choices-and-costs-the-short-run
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Socially Optimal Level of Output
Economics,Microeconomics
Equation

$\text{MSB} = \text{MSC}$

Latex Code
```
            \text{MSB} = \text{MSC}
        
```
Explanation

Latex code for Socially Optimal Level of Output.
- $\text{MSB}$ : Marginal Social Benefit
- $\text{MSC}$ : Marginal Social Cost
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- 8-1-production-choices-and-costs-the-short-run
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Total Costs
Economics,Microeconomics
Equation

$\text{TC} = \text{TFC} + \text{TVC}$

Latex Code
```
            \text{TC} = \text{TFC} + \text{TVC}
        
```
Explanation

Latex code for Socially Optimal Level of Output.
- $\text{TC}$ : Total Costs (TC)
- $\text{TFC}$ : Total Fixed Costs (TFC)
- $\text{TVC}$ : Total Variable Costs (TVC)
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- Total Variable Costs
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MacroEconomics

Investment
Economics,MacroEconomics
Equation

$I=I_{P}+I_{U}$

Latex Code
```
            I=I_{P}+I_{U}
        
```
Explanation

Latex code for the Investment. Investment during a period equals the sum of planned investment (I_P) and unplanned investment(I_U).
- $I$ : Investment
- $I_{P}$ : Planned investment
- $I_{U}$ : Unplanned investment
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- Principles Economics
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Aggregate Expenditure Without Government or Foreign Sectors
Economics,MacroEconomics
Equation

$\text{AE} = \text{C} + I_{P}$

Latex Code
```
            \text{AE} = \text{C} + I_{P}
        
```
Explanation

Latex code for the Investment. Aggregate expenditures equal the sum of consumption C and planned investment I_{P}. The aggregate expenditures function is the relationship of aggregate expenditures to the value of real GDP.
- $AE$ : Aggregate Expenditures
- $C$ : Consumption
- $I_{P}$ : Planned investment
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Marginal Propensity to Consume MPC
Economics,MacroEconomics
Equation

$\text{MPC} = \frac{\text{Change in Consumption}}{\text{Change in Income}}$

Latex Code
```
            \text{MPC} = \frac{\text{Change in Consumption}}{\text{Change in Income}}
        
```
Explanation

Latex code for the Marginal Propensity to Consume (MPC).
- $MPC$ : Marginal Propensity to Consume
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Marginal Propensity Save MPS
Economics,MacroEconomics
Equation

$\text{MPS} = \text{Marginal Propensity Save}$

Latex Code
```
            \text{MPS} = \frac{\text{Change in Saving}}{\text{Change in Income}}
        
```
Explanation

Latex code for the Marginal Propensity Save (MPS).
- $MPS$ : Marginal Propensity Save (MPS)
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Sum of Marginal Propensity to Save and Marginal Propensity to Consume
Economics,MacroEconomics
Equation

$\text{MPC} + \text{MPS} = 1$

Latex Code
```
            \text{MPC} + \text{MPS} = 1
        
```
Explanation

Latex code for the Sum of Marginal Propensity to Save and Marginal Propensity to Consume.
- $MPS$ : Marginal Propensity Save (MPS)
- $MPC$ : Marginal Propensity to Consume (MPC)
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Autonomous Spending Multiplier
Economics,MacroEconomics
Equation

$\text{Multiplier} = \frac{1}{1-MPC} = \frac{1}{MPS}$

Latex Code
```
            \text{Multiplier} = \frac{1}{1-MPC} = \frac{1}{MPS}
        
```
Explanation

Latex code for the Autonomous Spending Multiplier.
- $MPC$ : Marginal Propensity to Consume
- $MPS$ : Marginal Propensity Save
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- Principles Economics
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Balanced Budget Multiplier
Economics,MacroEconomics
Equation

$\text{Balanced Budget Multiplier}=\frac{1}{1-MPC}+\frac{-MPC}{1-MPC}=1$

Latex Code
```
            \text{Balanced Budget Multiplier} = \frac{1}{1-MPC} +  \frac{-MPC}{1-MPC}  = 1
        
```
Explanation

Latex code for the Autonomous Spending Multiplier.
- $MPC$ : Marginal Propensity to Consume
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Banks Reserve Ratio
Economics,MacroEconomics
Equation

$\text{Reserve Ratio} = \frac{\text{Bank Reserves}}{\text{Total Deposits}}$

Latex Code
```
            \text{Reserve Ratio} = \frac{\text{Bank Reserves}}{\text{Total Deposits}}
        
```
Explanation

Latex code for the Banks Reserve Ratio.
Related Documents
- Principles Economics
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Budget Deficit
Economics,MacroEconomics
Equation

$\text{Budget Deficit} = \text{Federal Government Spending} - \text{Tax Collections}$

Latex Code
```
            \text{Budget Deficit} = \text{Federal Government Spending} - \text{Tax Collections}
        
```
Explanation

Latex code for the Budget Deficit.
Related Documents
- Principles Economics
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Financial Account Balance
Economics,MacroEconomics
Equation

$\text{Financial Account Balance} = \text{Foreign Purchases of Home Assets} - \text{Home Purchases of Foreign Assets}$

Latex Code
```
            \text{Financial Account Balance} = \text{Foreign Purchases of Home Assets} - \text{Home Purchases of Foreign Assets}
        
```
Explanation

Latex code for the Financial Account Balance.
Related Documents
- Principles Economics
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Consumer Price Index CPI
Economics,MacroEconomics
Equation

$\text{CPI} = \frac{\text{Base Year Quantities} \times \text{Current Year Prices}}{\text{Base Year Quantities} \times \text{Base Year Prices}} \times 100$

Latex Code
```
            \text{CPI} = \frac{\text{Base Year Quantities} \times \text{Current Year Prices}}{\text{Base Year Quantities} \times \text{Base Year Prices}} \times 100
        
```
Explanation

Latex code for Consumer Price Index CPI.
Related Documents
- CPI Home : U.S. Bureau of Labor Statistics
- Investopedia: Consumer Price Index
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Consumption Function
Economics,MacroEconomics
Equation

$C=C_{a}+\text{MPC}(Y)$

Latex Code
```
            C = C_{a} + \text{MPC}(Y)               
        
```
Explanation

Latex code for Consumption Function.
Related Documents
- CPI Home : U.S. Bureau of Labor Statistics
- Investopedia: Consumer Price Index
Related Videos
Current-Account Balance
Economics,MacroEconomics
Equation

$\text{Current-Account Balance} + \text{Trade Balance} + \text{Services Balance} + \text{Unilateral}$

Latex Code
```
            \text{Current-Account Balance} + \text{Trade Balance} + \text{Services Balance} + \text{Unilateral}           
        
```
Explanation

Latex code for Current-Account Balance.
Related Documents
- CPI Home : U.S. Bureau of Labor Statistics
- Investopedia: Consumer Price Index
Related Videos
Equality of Leakages and Injections
Economics,MacroEconomics
Equation

$\text{S} + \text{T} + \text{M} = \text{I} + \text{G} + \text{X}$

Latex Code
```
            \text{S} + \text{T} + \text{M} = \text{I} + \text{G} + \text{X}  
        
```
Explanation

Latex code for Equality of Leakages and Injections. Injection and leakages in economics, Some transactions put money into the economy – that is, the money is being utilised elsewhere in the economy. These are injections. Some transactions take money out of the economy. That is, the money is not being utilised elsewhere in the economy. These are leakages.
- $\text{I}$ : Investment
- $\text{G}$ : Government Spending
- $\text{X}$ : Exports
Related Documents
- Why are leakages equal to injections?
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Equation of Exchange
Economics,MacroEconomics
Equation

$\text{MV} = \text{PQ}$

Latex Code
```
            \text{MV} = \text{PQ}
        
```
Explanation

Latex code for Equation of Exchange. The equation of exchange says simply that total spending on goods and services, measured as MV, equals total spending on goods and services, measured as PY (or nominal GDP). The equation of exchange is thus an identity, a mathematical expression that is true by definition.
- $\text{MV}$ : Total spending on goods and services, measured as Monetary Value
- $\text{PQ}$ : Total spending on goods and services, measured as PY (or nominal GDP)
Related Documents
- Investopedia: equation of exchange
- Monetary Policy and the Equation of Exchange
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Investment
Economics,MacroEconomics
Equation

$I=I_{P}+I_{U}$

Latex Code
```
            I=I_{P}+I_{U}
        
```
Explanation

Latex code for the Investment. Investment during a period equals the sum of planned investment (I_P) and unplanned investment(I_U).
- $I$ : Investment
- $I_{P}$ : Planned investment
- $I_{U}$ : Unplanned investment
Related Documents
- Principles Economics
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Aggregate Expenditure Without Government or Foreign Sectors
Economics,MacroEconomics
Equation

$\text{AE} = \text{C} + I_{P}$

Latex Code
```
            \text{AE} = \text{C} + I_{P}
        
```
Explanation

Latex code for the Investment. Aggregate expenditures equal the sum of consumption C and planned investment I_{P}. The aggregate expenditures function is the relationship of aggregate expenditures to the value of real GDP.
- $AE$ : Aggregate Expenditures
- $C$ : Consumption
- $I_{P}$ : Planned investment
Related Documents
- Principles Economics
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Marginal Propensity to Consume MPC
Economics,MacroEconomics
Equation

$\text{MPC} = \frac{\text{Change in Consumption}}{\text{Change in Income}}$

Latex Code
```
            \text{MPC} = \frac{\text{Change in Consumption}}{\text{Change in Income}}
        
```
Explanation

Latex code for the Marginal Propensity to Consume (MPC).
- $MPC$ : Marginal Propensity to Consume
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Marginal Propensity Save MPS
Economics,MacroEconomics
Equation

$\text{MPS} = \text{Marginal Propensity Save}$

Latex Code
```
            \text{MPS} = \frac{\text{Change in Saving}}{\text{Change in Income}}
        
```
Explanation

Latex code for the Marginal Propensity Save (MPS).
- $MPS$ : Marginal Propensity Save (MPS)
Related Documents
- Principles Economics
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Sum of Marginal Propensity to Save and Marginal Propensity to Consume
Economics,MacroEconomics
Equation

$\text{MPC} + \text{MPS} = 1$

Latex Code
```
            \text{MPC} + \text{MPS} = 1
        
```
Explanation

Latex code for the Sum of Marginal Propensity to Save and Marginal Propensity to Consume.
- $MPS$ : Marginal Propensity Save (MPS)
- $MPC$ : Marginal Propensity to Consume (MPC)
Related Documents
- Principles Economics
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Autonomous Spending Multiplier
Economics,MacroEconomics
Equation

$\text{Multiplier} = \frac{1}{1-MPC} = \frac{1}{MPS}$

Latex Code
```
            \text{Multiplier} = \frac{1}{1-MPC} = \frac{1}{MPS}
        
```
Explanation

Latex code for the Autonomous Spending Multiplier.
- $MPC$ : Marginal Propensity to Consume
- $MPS$ : Marginal Propensity Save
Related Documents
- Principles Economics
Related Videos
Balanced Budget Multiplier
Economics,MacroEconomics
Equation

$\text{Balanced Budget Multiplier}=\frac{1}{1-MPC}+\frac{-MPC}{1-MPC}=1$

Latex Code
```
            \text{Balanced Budget Multiplier} = \frac{1}{1-MPC} +  \frac{-MPC}{1-MPC}  = 1
        
```
Explanation

Latex code for the Autonomous Spending Multiplier.
- $MPC$ : Marginal Propensity to Consume
Related Documents
- Principles Economics
Related Videos
Banks Reserve Ratio
Economics,MacroEconomics
Equation

$\text{Reserve Ratio} = \frac{\text{Bank Reserves}}{\text{Total Deposits}}$

Latex Code
```
            \text{Reserve Ratio} = \frac{\text{Bank Reserves}}{\text{Total Deposits}}
        
```
Explanation

Latex code for the Banks Reserve Ratio.
Related Documents
- Principles Economics
Related Videos
Budget Deficit
Economics,MacroEconomics
Equation

$\text{Budget Deficit} = \text{Federal Government Spending} - \text{Tax Collections}$

Latex Code
```
            \text{Budget Deficit} = \text{Federal Government Spending} - \text{Tax Collections}
        
```
Explanation

Latex code for the Budget Deficit.
Related Documents
- Principles Economics
Related Videos
Financial Account Balance
Economics,MacroEconomics
Equation

$\text{Financial Account Balance} = \text{Foreign Purchases of Home Assets} - \text{Home Purchases of Foreign Assets}$

Latex Code
```
            \text{Financial Account Balance} = \text{Foreign Purchases of Home Assets} - \text{Home Purchases of Foreign Assets}
        
```
Explanation

Latex code for the Financial Account Balance.
Related Documents
- Principles Economics
Related Videos
Consumer Price Index CPI
Economics,MacroEconomics
Equation

$\text{CPI} = \frac{\text{Base Year Quantities} \times \text{Current Year Prices}}{\text{Base Year Quantities} \times \text{Base Year Prices}} \times 100$

Latex Code
```
            \text{CPI} = \frac{\text{Base Year Quantities} \times \text{Current Year Prices}}{\text{Base Year Quantities} \times \text{Base Year Prices}} \times 100
        
```
Explanation

Latex code for Consumer Price Index CPI.
Related Documents
- CPI Home : U.S. Bureau of Labor Statistics
- Investopedia: Consumer Price Index
Related Videos
Consumption Function
Economics,MacroEconomics
Equation

$C=C_{a}+\text{MPC}(Y)$

Latex Code
```
            C = C_{a} + \text{MPC}(Y)               
        
```
Explanation

Latex code for Consumption Function.
Related Documents
- CPI Home : U.S. Bureau of Labor Statistics
- Investopedia: Consumer Price Index
Related Videos
Current-Account Balance
Economics,MacroEconomics
Equation

$\text{Current-Account Balance} + \text{Trade Balance} + \text{Services Balance} + \text{Unilateral}$

Latex Code
```
            \text{Current-Account Balance} + \text{Trade Balance} + \text{Services Balance} + \text{Unilateral}           
        
```
Explanation

Latex code for Current-Account Balance.
Related Documents
- CPI Home : U.S. Bureau of Labor Statistics
- Investopedia: Consumer Price Index
Related Videos
Equality of Leakages and Injections
Economics,MacroEconomics
Equation

$\text{S} + \text{T} + \text{M} = \text{I} + \text{G} + \text{X}$

Latex Code
```
            \text{S} + \text{T} + \text{M} = \text{I} + \text{G} + \text{X}  
        
```
Explanation

Latex code for Equality of Leakages and Injections. Injection and leakages in economics, Some transactions put money into the economy – that is, the money is being utilised elsewhere in the economy. These are injections. Some transactions take money out of the economy. That is, the money is not being utilised elsewhere in the economy. These are leakages.
- $\text{I}$ : Investment
- $\text{G}$ : Government Spending
- $\text{X}$ : Exports
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- Why are leakages equal to injections?
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Equation of Exchange
Economics,MacroEconomics
Equation

$\text{MV} = \text{PQ}$

Latex Code
```
            \text{MV} = \text{PQ}
        
```
Explanation

Latex code for Equation of Exchange. The equation of exchange says simply that total spending on goods and services, measured as MV, equals total spending on goods and services, measured as PY (or nominal GDP). The equation of exchange is thus an identity, a mathematical expression that is true by definition.
- $\text{MV}$ : Total spending on goods and services, measured as Monetary Value
- $\text{PQ}$ : Total spending on goods and services, measured as PY (or nominal GDP)
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Gross Domestic Product GDP
Economics,MacroEconomics
Equation

$\text{GDP}=\text{C}+\text{I}+\text{G}+(\text{X}-\text{M})$

Latex Code
```
            \text{GDP}= \text{C} + \text{G} + \text{I} + \text{NX}=\text{C}+\text{I}+\text{G}+(\text{X}-\text{M}) \\
            \text{GDP} = \text{Total National Income} + \text{Sales Taxes} + \text{Depreciation} + \text{Net Foreign Factor Income}
        
```
Explanation

Latex code for Gross Domestic Product. There are two primary methods or formulas by which GDP can be determined: 1. Expenditure Approach, The expenditure approach is the most commonly used GDP formula, which is based on the money spent by various groups that participate in the economy. GDP = C + G + I + NX. 2. Income Approach, This GDP formula takes the total income generated by the goods and services produced. GDP = Total National Income + Sales Taxes + Depreciation + Net Foreign Factor Income
- $\text{GDP}$ : Gross Domestic Product
- $\text{C}$ : consumption or all private consumer spending within a country’s economy, including, durable goods (items with a lifespan greater than three years), non-durable goods (food & clothing), and services.
- $\text{G}$ : total government expenditures, including salaries of government employees, road construction/repair, public schools, and military expenditure.
- $\text{NX}$ : net exports or a country's total exports less total imports
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Gross Domestic Product Deflator

Economics,MacroEconomics

Equation

$\text{GDP Deflator}= \frac{\text{Current Year Quantities} \times \text{Current Year Prices}}{\text{Current Year Quantities} \times \text{Base Year Prices}} \times 100$

Latex Code

            \text{GDP Deflator}= \frac{\text{Current Year Quantities} \times \text{Current Year Prices}}{\text{Current Year Quantities} \times \text{Base Year Prices}} \times 100

Explanation

Latex code for Gross Domestic Product Deflator.

Gross Domestic Product Deflator

Economics,MacroEconomics

Equation

$\text{GDP Deflator}= \frac{\text{Current Year Quantities} \times \text{Current Year Prices}}{\text{Current Year Quantities} \times \text{Base Year Prices}} \times 100$

Latex Code

            \text{GDP Deflator}= \frac{\text{Current Year Quantities} \times \text{Current Year Prices}}{\text{Current Year Quantities} \times \text{Base Year Prices}} \times 100

Explanation

Latex code for Gross Domestic Product Deflator.

3. FINANCIAL REPORTING & ANALYSIS

Basic EPS
Math,Finance
Equation
$$ \text{Basic EPS}=\frac{\text{Net income} - \text{Preferred dividends}}{\text{Weighted average number of shares outstanding}} $$

Latex Code
```
            \text{Basic EPS}=\frac{\text{Net income} - \text{Preferred dividends}}{\text{Weighted average number of shares outstanding}}
        
```
Explanation

Explanation for Basic EPS
- $$\text{Basic EPS}$$: Basic Earning Per Share
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Diluted EPS
Math,Finance
Equation
$$\text{Diluted EPS}=\frac{\text{Net Income}}{\text{Weighted average number of shares outstanding} - \text{Net Common Shares that Would Have Been Issued at Conversion}}$$

Latex Code
```
            \text{Diluted EPS}=\frac{\text{Net Income}}{\text{Weighted average number of shares outstanding} - \text{Net Common Shares that Would Have Been Issued at Conversion}}
        
```
Explanation

Explanation for Diluted EPS, if preferred Shares is converted to ordinary shares.
- $$\text{Diluted EPS}$$: Diluted Earning Per Share
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Balance Sheet
Math,Finance
Equation
$$\text{Assets}=\text{Liabilities} + \text{Equity}$$

Latex Code
```
            \text{Assets}=\text{Liabilities} + \text{Equity}
        
```
Explanation
- $$\text{Assets}$$: Assets
- $$\text{Liabilities}$$: Liabilities
- $$\text{Equity}$$: Equity
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Cash Flow Performance Ratio

Cash Flow To Revenue Ratio
Math,Finance
Equation
$$\text{Cash Flow to Revenue Ratio}=\frac{\text{Cash Flow from Operating}}{\text{Net Revenue}}$$

Latex Code
```
            \text{Cash Flow to Revenue Ratio}=\frac{\text{Cash Flow from Operating}}{\text{Net Revenue}}
        
```
Explanation
- $$\text{CFO}$$: Cash Flow from Operating
- $$\text{Net Revenue}$$: Net Revenue
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Cash Return On Assets
Math,Finance
Equation
$$\text{Cash Return On Assets}=\frac{\text{CFO}}{\text{Average Total Assets}}$$

Latex Code
```
            \text{Cash Return On Assets}=\frac{\text{CFO}}{\text{Average Total Assets}}
        
```
Explanation
- $$\text{CFO}$$: Cash Flow from Operating
- $$\text{Average Total Assets}$$: Average Total Assets
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Cash To Income
Math,Finance
Equation
$$\text{Cash To Income}=\frac{\text{CFO}}{\text{Operating Income}}$$

Latex Code
```
            \text{Cash To Income}=\frac{\text{CFO}}{\text{Operating Income}}
        
```
Explanation
- $$\text{CFO}$$: Cash Flow from Operating
- $$\text{Operating Income}$$: Operating Income
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Cash flow Per Share
Math,Finance
Equation
$$\text{Cash flow Per Share}=\frac{\text{CFO-Preferred Dividents}}{\text{Number of Common Shares Outstanding}}$$

Latex Code
```
            \text{Cash flow Per Share}=\frac{\text{CFO-Preferred Dividents}}{\text{Number of Common Shares Outstanding}}
        
```
Explanation
- $$\text{CFO}$$: Cash Flow from Operating
- $$\text{Preferred Dividents}$$: Preferred Dividents
- $$\text{Number of Common Shares Outstanding}$$: Number of Common Shares Outstanding
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Free Cash Flow to the Firm
Math,Finance
Equation
$$FCFF=NI +NCC + Int(1-T) -FCInv-WCInv$$
$$=CFO+Int(1-T)-FCInv$$

Latex Code
```
            FCFF=NI +NCC + Int(1-T) -FCInv-WCInv \\
            =CFO+Int(1-T)-FCInv
        
```
Explanation
- $$\text{NI}$$: Net Income
- $$\text{NCC}$$: Non-Cash Charges
- $$\text{Int}$$: Interest Expense
- $$\text{FCInv}$$: Capital Expenditures
- $$\text{WCInv}$$: Working capital expenditure
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Debt Coverage Ratio
Math,Finance
Equation
$$\text{Debt Coverage Ratio}=\frac{\text{CFO}}{\text{Total Debt}}$$

Latex Code
```
            \text{Debt Coverage Ratio}=\frac{\text{CFO}}{\text{Total Debt}}
        
```
Explanation
- $$\text{CFO}$$: Cash Flow from Operating
- $$\text{Total Debt}$$: Total Debt
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Interest coverage ratio
Math,Finance
Equation
$$\text{Interest coverage ratio}=\frac{\text{CFO} + \text{Interest Paid} + \text{Taxes Paid}}{\text{Interest Paid}}$$

Latex Code
```
            \text{Interest coverage ratio}=\frac{\text{CFO} + \text{Interest Paid} + \text{Taxes Paid}}{\text{Interest Paid}}
        
```
Explanation
- $$\text{CFO}$$: Cash Flow from Operating
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Reinvestment Coverage Ratio
Math,Finance
Equation
$$\text{Reinvestment Coverage Ratio}=\frac{\text{CFO}}{\text{Cash Paid for Long Term Asset}}$$

Latex Code
```
            \text{Reinvestment Coverage Ratio}=\frac{\text{CFO}}{\text{Cash Paid for Long Term Asset}}
        
```
Explanation
- $$\text{CFO}$$: Cash Flow from Operating
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Debt Payment Coverage Ratio
Math,Finance
Equation
$$\text{Debt Payment Coverage Ratio}=\frac{\text{CFO}}{\text{Cash Paid for Long Term Debt Repayment}}$$

Latex Code
```
            \text{Debt Payment Coverage Ratio}=\frac{\text{CFO}}{\text{Cash Paid for Long Term Debt Repayment}}
        
```
Explanation
- $$\text{CFO}$$: Cash Flow from Operating
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Activity Ratio

Inventory Turnover
Math,Finance
Equation
$$\text{Inventory Turnover}=\frac{\text{Cost of Goods Sold}}{\text{Average Inventory}}$$

Latex Code
```
            \text{Inventory Turnover}=\frac{\text{Cost of Goods Sold}}{\text{Average Inventory}}
        
```
Explanation
- $$\text{Inventory Turnover}$$: Inventory Turnover
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Days of Inventory On Hand (DOH)
Math,Finance
Equation
$$\text{Days of Inventory On Hand}=\frac{\text{Average Inventory}}{\text{Cost of Goods Sold}} \times 365$$

Latex Code
```
            \text{Days of Inventory On Hand}=\frac{\text{Average Inventory}}{\text{Cost of Goods Sold}} \times 365
        
```
Explanation
- $$\text{Days of Inventory On Hand}$$: Days of Inventory On Hand
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Receivables Turnover
Math,Finance
Equation
$$\text{Receivables Turnover}=\frac{\text{Revenue}}{\text{Average Receivables}}$$

Latex Code
```
            \text{Receivables Turnover}=\frac{\text{Revenue}}{\text{Average Receivables}}
        
```
Explanation
- $$\text{Receivables Turnover}$$: Receivables Turnover
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Days of Sales Outstanding
Math,Finance
Equation
$$\text{Days of Sales Outstanding}=\frac{\text{Average Receivables}}{\text{Revenue}} \times 365$$

Latex Code
```
            \text{Days of Sales Outstanding}=\frac{\text{Average Receivables}}{\text{Revenue}} \times 365
        
```
Explanation
- $$\text{Days of Sales Outstanding}$$: Days of Sales Outstanding
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Navigation

THE TIME VALUE OF MONEY

Future Value

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Present Value

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Effective Annual Rate

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Continuous Compounding

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Ordinary Annuity

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Annuity Due

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THE TIME VALUE OF MONEY

Perpetuity

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STATISTICAL CONCEPT AND MARKET RETURNS

Mean and Variance

Standard Deviation

Probability Distributions

Binomial Distribution

Poisson Distribution

Normal Gaussian Distribution

Chi-Square Test

3. Advanced Statistics

Sum of Random Variables

Covariance

Gamma Distribution

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Fisher Skewness

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Kurtosis

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Two-asset portfolio

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Three-asset portfolio

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2. Economics

MicroEconomics

1. Microeconomics

Simple Interest

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Compound Interest

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Effective Rate

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Future Value of Ordinary Annuities

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Annuities Due

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Present Value of Ordinary Annuities

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