Dumping my notes here.

MR = P_e (1 + 1/η) η = dQ/dP * P_e/Q_e

Price is elastic when 0 <= Q < a/2b where a and b are coefficients of the demand function

INPUT MAXIMIZATION MR / Product of input a = Marginal Expenditure of input a

MP_L / P_L = MP_K / P_K

Elasticity of output for Cobb-Douglas equals the exponent of the respective input E.g. Q_1 = 100 * L^0.7 * K^0.4 increase labour by 1%: Q_2 = 100(1.01L)^0.7 * K^0.4 Q_2 = 1.006989(100L^0.7 * K^0.4) Q_2 ~= 1.007Q -> 0.7% increase (exponent)

Economies of Scope When it is cheaper to produce quantities of two products together How much is saved as a percentage of the new cost (OLD COST - NEW COST) / NEW COST

In PC, profit maximizing level is when P = MC

markup equal to −1/(1 + η) markup % = P / MC

in fixed proportions, MC = MR_A + MR_B as long as either MR is > 0

Cournot solution Set dProfit/dQ_a/b = 0 for both companies where Q_a/b is the respective Quantity for each company (e.g. TR_a = XQ_A + m(Q_a + Q_b)Q_a ) Substitute equations and voila Price leader Using the Q_b = … equation, sub into P= equation e.g. Q = Q_a + Q_b where Q_b is the substituted equation

Advertising expenditures are optimal if an additional dollar spent on ads increases net profit (NOT MR) by one dollar. MR from $1 of advertising should equal elasticity of demand curve

Price Discrimination Optimal MR_1 = MR_2 P_1(1 + 1 / ped_1) = P_2(1 + 1 / ped_2) P_1 / P_2 = [1 + (1 / ped_2)] / [1 + (1 / ped_1)]

First degree Charging at demand curve Second degree By usage. Less/q as q increases Third degree Discounting distinct separable markets set MR_1 = MC = MR_2 Peak load pricing

Pricing Strategy (Coupons) MR_R = MR_S = MC P(1 + 1 / PED_R) = (P - X)(1 + 1 / PED_S)= MC. X is discount value PED_R for those who don’t use coupons. PED_S for those who use coupons.

Two part tariff Entry fee = consumer surplus where P = MC Per use fee found by P = MC

Profit = R - Fixed Costs - Dis-utility of Manager as $

When calculating utility with probabilities, first calculate utility of all wealths and then multiply by the probabilities

When there are big firms and small firms, set MC_i = P to first find q_i and then * by # to get Q_small Then do Q - Q_small to get Q_big which you can use to find P

variance = weight * (val_1 - weighted_mean)^2 + … std_dev = sqrt(variance)