1. Producer Theory 1. Technology yi =input of good i, y =output of good i, i= yi-yi=net output, y yn) is a production plan Production possibility set Y=technologically feasible production plans yE Rn) y E Y is technologically efficient if there is no yE Y s.t. y>y

This formula applies to any type of firms in the output market 1. Competitive Output Market Competitive industry: Many firms: Firms are independent of each other in decision making Identical product: Each firm faces a horizontal demand curve at the market price Free entry: Zero profit in the long run A competitive firm takes the market price as given. For a given market price p

Production Plans with Multiple Outputs Lety≡(m,,…,ym) be a net output vector, YArn be a convex set,G:Y→R be twice differentiable Production possibility set:{y∈Y|G(y)≤0} Assumption 1.1. Gy (y)>0, Vi,yEY. Proposition 1. 12. Production frontier yEY G(y)=0 contains technologically efficient production plans Definition 1.1. Marginal rate of transformation

Problem set 3 Micro Susen Wang Try to do most problems in MWG(1995), Chapters 7-9 Question 3.1.(Mixed-Strategy Nash Equilibrium). A principal hires an agent to perform some service at a price(which is supposed to equal the cost of the service The principal and the agent have initial

Problem set 1 Micro Theory S. Wang Question1.1. Show that“f(X)=f(x),Vx∈R,A>1” implies“f(A)= Af(x),Vx∈R,A>0.” estion 1.2. Use a Lagrange function to solve c(w1, w2, y) for the following problem

Then =1-91=1(3+:2)(3+2n 可=-1-3)=1(4-+2)(1-2+a With 1 0 O: Thus, in equilibrium, we must have ai=.2. In fact, the two firms must sit in the middle By Proposition 2.1, Pi=p?=c Discussion

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