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min{2x, 3y} meaning
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you need 2/3 of y for 1 hour of x
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how to write minimum utility constraints
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x + y = 24
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minimum utility optimizing set up
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2x = 3y
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How to solve elasticity problems with multivariable demand functions
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Take out factor, put variable in the numerator, and put the entire demand function in the denominator
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How to solve elasticity problems with fraction demand functions
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partial derivatives of numerator and denominator
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budget equation
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px + py = M
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Cournot competition profit function for firm 1
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(profit function)q1 - q1
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nash equilibrium steps
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take the derivative of the profit function and substitute since q1=q2
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Monopolist profit function
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price*Q - cost
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monopolist profit maximization
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take the derivative of the profit function and solve for Q, then substitute into price
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market price and quantity
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P = MC
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MC derived from total cost
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take the derivative to get marginal
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dominant strategy
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no matter what the other player does, you can't do worse
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cartel sustainability
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cheating profit - coop profit <= 1/i (profit coop - profit Nash)
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vertical quality
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quality of a product that is the same for all customers
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joint profit function
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price * quantity - cost(half quantity) - cost(half quantity)
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cheating profit function
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(overall price function - quantity of cheated firm) cheater firm quantity - cheater firm cost
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nash equilibrium profit function (best response function)
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(price function minus quantity of other firm) * quantity of firm 1 - cost of firm 1. This is then derived and substituted
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effect of merging firms
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marginal revenue of firm 1 becomes profit of combined firm
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indifferent consumer
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believes each product is worth buying
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moral hazard
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a hidden action that benefits one party at the expense of another
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adverse selection
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one party in a negotiation has relevant info another party lacks
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grim trigger strategy
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Cooperate until opponent defect, then defect forever
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utility maximization representation
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u(x,y) = ax + by
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Market rate of substitution formula
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marginal utility x / marginal utility y
a(x^a-1)(y^b)/b(x^a)y(^b-1)
a(x^a-1)(y^b)/b(x^a)y(^b-1)
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Elasticity formula
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dX/dY * Y/X
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Indexes for market competition
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four-firm concentration ratio, hhi, lerner index
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5 key perfect comp assumptions
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lots of buyers and sellers, similar products, perfect info, no transaction costs, free entry
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oligopoly models
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cournot, stackelberg, bertrand, hotelling
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bertrand paradox
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with few firms and high barriers, firms price at marginal cost
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Subgame Perfect Nash Equilibrium
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a set of strategies that are a nash equilibrium in every subgame of the overall game
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pricing strategies
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price discrimination, price matching, two-part tariff
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Risk preferences
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risk averse, risk neutral, risk seeking
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loss aversion
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response to losses is stronger than the response to gains
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Hotelling representatoin
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product location on a line
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value of buying with hotelling model
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v0 = r - tx - p0
v1 = r - t(1-x) - p1
v1 = r - t(1-x) - p1
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hotelling variables
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r = quality, t = transportation, p = price
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value and location relationship in hotelling
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value from consumption is lower the farther from the location
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high t meaning
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people are frustrated with the availability of a characteristic
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indifferent consumer location
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set v0 equal to v1 and solve
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expected profit function
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probability 1(profit function 1) + probability 2(profit function 2)
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