ECONOMICS Equation Formula Directory Database Latex Code & Learning Explanation

Allocative Efficiency Condition

#Economics #Microeconomics

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

Annuities Due

#Economics

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

Average Fixed Cost

#Economics #Microeconomics

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

Average Product

#Economics #Microeconomics

$$\text{AP} = \frac{\text{Total Product}}{\text{Quantity of Input}}$$

Average Revenue

#Economics #Microeconomics

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

Average Total Cost

#Economics #Microeconomics

$$\text{Average Total Cost(ATC)} = \frac{\text{Total Cost (TC)}}{\text{Quantity of Output (Q)}}$$

Average Variable Cost

#Economics #Microeconomics

$$\text{Average Variable Cost(AVC)} = \frac{\text{Total Variable Cost (TVC)}}{\text{Quantity of Output (Q)}}$$

Compound Interest

#Economics

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

Cross-Price Elasticity of Demand

#Economics #Microeconomics

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

Effective Rate

#Economics

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

Elasticity of Supply

#Economics #Microeconomics

$$\text{Elasticity of Supply} = \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}$$

Factor of Production Hiring Rule

#Economics #Microeconomics

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

Future Value of Ordinary Annuities

#Economics

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

Marginal Cost

#Economics #Microeconomics

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

Marginal Revenue Product

#Economics #Microeconomics

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

Present Value of Ordinary Annuities

#Economics

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

Simple Interest

#Economics

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

Distributive Efficiency Condition

#Economics #Microeconomics

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

Gini Coefficient

#Economics #Microeconomics

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

Investment

#Economics #MacroEconomics

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

Marginal Factor Cost MFC

#Economics #Microeconomics

$$\text{MFC} = \frac{\Delta \text{TC}}{\Delta \text{f}}$$

Marginal Product of Labor

#Economics #Microeconomics

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

Marginal Revenue

#Economics #Microeconomics

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

Marginal Revenue Product of Labor MRPL

#Economics #Microeconomics

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

Optimal Combination of Resources Condition

#Economics #Microeconomics

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

Optimal Consumption Rule

#Economics #Microeconomics

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

Price Elasticity of Demand

#Economics #Microeconomics

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

Price for a Competitive Firm

#Economics #Microeconomics

$$P = MR$$

Production Efficiency Condition

#Economics #Microeconomics

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

Profit

#Economics #Microeconomics

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

Profit-Maximizing Output Level

#Economics #Microeconomics

$$MR = MC$$

Slope of the Total Product Curve

#Economics #Microeconomics

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

Socially Optimal Level of Output

#Economics #Microeconomics

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

Total Costs

#Economics #Microeconomics

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

Autonomous Spending Multiplier

#Economics #MacroEconomics

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

Balanced Budget Multiplier

#Economics #MacroEconomics

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

Banks Reserve Ratio

#Economics #MacroEconomics

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

Calls and Puts with Different Strikes

#Financial #Economics

$$K_{1} < K_{2} \\ 0 \le c(K_{1}) - c(K_{2}) \le (K_{2} - K_{1})e^{-rT} \\ 0 \le p(K_{2}) - p(K_{1}) \le (K_{2}) - K_{1})e^{-rT} \\ \frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \ge \frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\ \frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \le \frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}$$

Consumer Price Index CPI

#Economics #MacroEconomics

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

Consumption Function

#Economics #MacroEconomics

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

Equality of Leakages and Injections

#Economics #MacroEconomics

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

Equation of Exchange

#Economics #MacroEconomics

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

Forwards

#Financial #Economics

$$F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\text{Dividends}) = S_{t}e^{(r-\delta)(T-t)}$$

Gross Domestic Product Deflator

#Economics #MacroEconomics

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

Merchandise Trade Balance

#Economics #MacroEconomics

$$\text{Merchandise Trade Balance}=\text{Value of Merchandise Exports} - \text{Value of Merchandise Imports}$$

Nominal Interest Rate

#Economics #MacroEconomics

$$\text{Nominal Interest Rate}=\text{Real Interest Rate} + \text{Anticipated Inflation}$$

Put-Call Parity

#Financial #Economics

$$c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}$$

Real GDP

#Economics #MacroEconomics

$$\text{Real GDP}=\frac{Nominal GDP}{CPI for the same year as the nominal figure} \times 100$$

Real Interest Rate

#Economics #MacroEconomics

$$\text{Real Interest Rate} = \text{Nominal Interest Rate} – \text{Anticipated Inflation}$$

Tax Multiplier

#Economics #MacroEconomics

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

Unemployment Rate

#Economics #MacroEconomics

$$\text{Unemployment Rate} = \frac{\text{Unemployed}}{\text{Labor Force}}$$

Asian Options

#Financial #Economics

$$A(T) = \frac{1}{n} \sum S(ih) \\ G(T) = [\prod S(ih)]^{\frac{1}{n}}$$

Black-Derman-Toy BDT

#Financial #Economics

$$\text{First Node: 1-year bond price} \\ P_{0} = \frac{1}{1 + R_{0}} \\ \text{Second Node} \\ P_{1} = \frac{1}{1+R_{0}} [\frac{1}{2} P(1,2,r_{u}) + \frac{1}{2} P(1,2,r_{d})] \\ = \frac{1}{1+R_{0}} [\frac{1}{2(1 + R_{1}e^{2\sigma_{1}})} + \frac{1}{2(1 + R_{1})}] \\ R_{0} = \frac{1}{2} \ln (\frac{R_{1} e^{2\sigma_{1}} }{R_{1}})$$

Bonds and Interest Rates

#Financial #Economics

$$P(0, S) = \frac{1}{[1 + r(0, s)]^{s}} \text{or} e^{-r(0,s)s} \\ \text{Forward bond price} \\ F_{t,T}[P(T, T+s)] = \frac{P(t, T+s)}{P(t, T)} \\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)$$

Call and Put Price Bounds

#Financial #Economics

$$(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \le c(S_{t},K,t,T) \le F^{P}_{t,T}(S) \\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \le p(S_{t},K,t,T) \le Ke^{-r(T-t)} \\ c(S_{t},K,t,T) \le C(S_{t},K,t,T) \le S_{t} \\ p(S_{t},K,t,T) \le P(S_{t},K,t,T) \le K$$

Calls and Puts Arbitrage

#Financial #Economics

$$K_{1} < K_{2} < K_{3} \\ K_{2} = \lambda K_{1} + (1 - \lambda) K_{3} \\ \lambda = \frac{K_{3} - K_{2}}{K_{3} - K_{1}}$$

Cox-Ingersoll-Ross CIR

#Financial #Economics

$$\mathrm{d} r(t) = a[b - r(t)] \mathrm{d} t + \sigma \sqrt{r(t)} \mathrm{d} Z(t) \\ P(r, t, T) = A(T-t)e^{-rB(T-t)} \\ \gamma = \sqrt{(a-\bar{\phi})^{2} + 2 \sigma^{2}} \\ q(r, t, T) = \sigma \sqrt{r} B(T-t) \\ \text{yield to maturity} \\ \frac{2ab}{ a - \bar{\phi} + \gamma}$$

Early Exercise for American Options

#Financial #Economics

$$P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)$$

Geometric Brownian Motion

#Financial #Economics

$$Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\mu t + \sigma Z(t)]} \\ E(e^{kU}) = e^{kE(U) + \frac{1}{2}k^{2}\text{Var}(U)} \\ E[Y^{k}(t)] = Y^{k}(0) e^{(k\mu + \frac{1}{2}k^{2}\sigma^{2})t} \\ \ln Y(t) \sim N(\ln Y(0) + \mu t, \sigma^{2} t)$$

Geometric Brownian Motion SDEs

#Financial #Economics

$$\mathrm{d}Y(t) = \mu Y(t)dt + \sigma Y(t) \mathrm{d}Z(t) \\ \mathrm{d}[\ln Y(t)] = (\mu - \frac{\sigma^2}{2}) \mathrm{d}t + \sigma \mathrm{d}Z(t) \\ Y(t) = T(0) e^{(\mu - \frac{\sigma^2}{2})t + \sigma Z(t)}$$

Ito Lemma

#Financial #Economics

$$\mathrm{d}X(t) = a(t, X(t)) \mathrm{d}t + b(t, X(t))\mathrm{d} Z(t) \\ Y(t) = f(t, X(t)) \mathrm{d}t \\ \mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\mathrm{d} X(t) + \frac{1}{2} f_{xx}(t, X(t))[\mathrm{d}X(t)]^{2} \\ [\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\mathrm{d} t$$

Monte-Carlo Simulations

#Financial #Economics

$$S(T) = S(0) e^{(a - \delta - \frac{\sigma^2}{2})T + \sigma \sqrt{T} z} \\ S(T) = S(t) e^{(a - \delta - \frac{\sigma^2}{2})(T-t) + \sigma (Z(T) - Z(t))} \\ \text{Variance} \\ e^{-2rT} \times \frac{s^{2}}{n} \\ s^{2} = \frac{1}{n-1} \sum [(g(S_{i}) - \bar{g})]^{2}$$

Risk-Neutral Valuation and Power Contracts

#Financial #Economics

$$\frac{\mathrm{d}S(t)}{S(t)} = (r - \delta) \mathrm{d}t + \sigma \mathrm{d} \tilt{Z}(t) \\ \tilt{Z}(t) = Z(t) + \phi t \\ V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\ F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\delta) + \frac{1}{2} a(a-1)\sigma^{2})(T-t)}$$

Sharpe Ratio

#Financial #Economics

$$\frac{\mathrm{d}X(t)}{X(t)} = m \mathrm{d}t + s \mathrm{d}Z(t) \\ \phi = \frac{m + \delta -r }{s} \\ \phi = \frac{a - r}{\sigma}$$

Standard Brownian Motion

#Financial #Economics

$$Z(t) \sim N(0, t) \\ Z(t+s) - Z(t) \sim N(0, s) \\ Z(t+s) \sim N(Z(t), s)$$

Stock Prices as Geometric Brownian Motion

#Financial #Economics

$$\frac{\mathrm{d}S(t)}{S(t)} = (a - \delta) \mathrm{d}t + \sigma \mathrm{d}Z(t) \\ S(t) = S(0) e^{(a - \delta - \frac{\sigma^{2}}{2})t + \sigma Z(t)} \\ \mathrm{d}[\ln S(t)] = (a - \delta - \frac{\sigma^{2}}{2}) \mathrm{d}t + \sigma \sigma \mathrm{d} Z(t) \\ S(t) \sim \ln( \ln S(0) + (a - \delta - \frac{\sigma^2}{2})t, \sigma^{2}t)$$

Varying Times to Expiration

#Financial #Economics

$$T_{2} \ge T_{1} \\ C(S_{t},K,t,T_{2}) \ge C(S_{t},K,t,T_{1}) \le S_{t} \\ P(S_{t},K,t,T_{2}) \ge P(S_{t},K,t,T_{1}) \le S_{t}$$

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