Micro Term 2

What are the four different oligopoly models?

Cournot: Simultaneous - firms choose output quantities

Collusion: Firms cooperate to max joint profits by limiting total output

Bertrand: Simultaneous - firms set prices

Stackelberg: Sequential - leader chooses output first, follower follows

What is the Cournot model?

Cournot: Simultaneous - firms choose output quantities

What is the Bertrand model?

Bertrand: Simultaneous - firms set prices

What is the Stackelberg model?

Stackelberg: Sequential - leader chooses output first, follower follows

What is the equation for the isoprofit line?

Isoprofit: $\pi=py-wL$

How do you solve for cost minimisation?

Set TRS = price ratio ($-\frac{w1}{w2}$ )

What’s the formula for own-price elasticity?

PED ($\epsilon$) = $\frac{dy}{dp}\cdot\frac{p}{y}$

What is the profit-maximising formula for a monopoly?

MR = MC

p = $\frac{MC}{\left(1-\frac{1}{\epsilon}\right)}$

What is the markup factor formula for a monopoly?

Markup factor = $\frac{1}{1-\frac{1}{\epsilon}}$

What is the profit max condition for a monopoly?

What is the profit max condition for a competitive market?

p = MC

In the long-run:

p = min{AC}

What is the socially optimum condition for a monopoly?

p = MC

For an oligopoly under collusion what are the strategies that make collusion stable?

1. Cooperation phase

2. Punishment phase

Cooperate profit: $\frac{\pi^{M}}{1-\delta}$

Deviation profit: $\pi^{D}+\delta\cdot\frac{\pi^{Cour}}{1-\delta}$

Collusion is sustainable if cooperate profit >= deviation profit

How do you solve for the Cournot equilibrium in an Oligopoly?

Firm 1 profit max: $\pi$1 = P(y1+y2))y1 - c(y1)

Same for Firm 2

Solve for y1 as a function of y2 and y2 as a finction of y1

Substitute y2 as a function of y1 into y1 as a function of y2

Solve for y1*

Solve for y2*

How do you solve for the Stackelberg equilibrium in an Oligopoly?

Find followers reaction function (y^s2)

Find leaders prof max: P(y1+y^s2) - c(y1)

Substitute y^s2 into leaders prof max

Find F.O.C of leaders prof max, set equal to zero and solve for y1

Substitute y1 back into followers reaction function

For a production function f(x1,x2) = min{ax1,bx2} what are the conditional factor demands for y units of output? What’s the cost function?

x1 = $\frac{y}{a}$

x2 = $\frac{y}{b}$

c(w1,w2,y) = $y\left(\frac{w1}{a}+\frac{w2}{b}\right)$

What is the consumer surplus and dead weight loss in a monopoly diagram?

How do you solve for Cobb-Douglas conditional factor demands, cost function and optimal factor demands?

Conditional factor demands: TRS = -$\frac{w1}{w2}$ Solve for x1 in terms of x2, w1, w2 and then subsitute into the production function to solve for x1* and x2*

Cost function: Substitute x1* and x2* into the total cost equation: c = x1*w1 + x2*w2

Optimal factor demands: Profit max. then find F.O.Cs and substitute to solve for L* and K*

How do you solve for Perfect Complements conditional factor demands, and cost function?

Conditional factor demands: y = ax1 = bx2, solve for x1* = y/a and x2* = y/b

Cost function: substitute conditional factor demands into total cost equation C = w1*x1 + w2*x2

How do you solve for Perfect Substitutes conditional factor demands and cost function?

Conditional factor demands: firm exclusively uses whichever input is the most cost effective. TRS = -w1/w2. If a/b < w1/w2 then only use x2 as w2 < a/b*w1

Cost function: c = min{$\frac{w1}{a},\frac{w2}{b}$ }*y