Calculate the consumer and producer surplus and the

Question

Question 1: Given the following demand, supply and marginal revenue curves, calculate the equilibrium output and price under Perfect Competition, Monopoly, and Cournot Duopoly. In addition, calculate the consumer and producer surplus in each market and discuss the efficiency implications of the different market structures.

a. Q = 820 - 1000P

b. P = -Q/1000 + .82

c. MR = Q/500 + .82

d. MC = 0.28

e. Cournot:

       i. TR₁ = P*q₁ = q₁² + q₁*q₂/1000 + 0.82q₁

       ii. TR₂ = P*2 = q₂² + q₂*q₁/1000 + 0.82q₂

       iii. MR₁ = 2q₁ + q₂/1000 + 0.82

       iv. MR₁ = 2q₂ + q₁/1000 + 0.82

Question 2: Utilizing the following functions determine the equilibrium output and price for a perfectly competitive equilibrium. In addition, calculate the consumer and producer surplus, and the deadweight loss after a tax on producers of $1000 is imposed.

a. Demand: P=10000-100Q

b. Marginal Cost: MC=$2500

Question 3: Given the following production function, factor prices, and the firm's input demand functions, derive the firm's total cost function and least cost combination of K and L.

a. In addition, calculate the change in the least cost combination when wages increase to$5. Ensure to show your results graphically. (Min TC Given Q)

b. Finally, using the total cost from the original producer solution, calculate the change in Q, K, and L from the wage increase. (Max Q Given TC)

c. Q=K*L

d. L* =  (Q*r/w)^0.5 & K* = (Q*w/r)0.5

e. L* =  TC/2*w & K* = TC/2*r

  i. w=$4

  ii. r=$13

  iii. Q=200