Demand function

Demand function

QA=75-P

QB=25-4P

500 identical consumers with each following individual demand function

Market Demand: Q= 500(QA+QB) =500(75-P + 25-4P)= 500(100-5P)= 5000-2500P

Production Function: Q (L,K) =0.5L^0.5K^2

1. 1. Suppose that all markets are competitive with one representative firm in the output market.
2. a. Derive the market demand for the output.
3. b. Draw an isoquant curve for the output by connecting multiple input combinations.
4. c. Derive the marginal rate of technical substitution (MRTS) from the production function.
5. d. Given the input prices, and , express and draw the isocost line.
6. e. Derive the total cost function of output for both short run and long run.
7. f. Derive the marginal cost and average cost for both short run and long run.
8. g. Derive the supply curve of output for both short run and long run.
9. h. Characterize the short run competitive equilibrium for the economy. Be clear about the equilibrium prices of output and inputs, the quantities of output and inputs.
10. i. Characterize the long run competitive equilibrium for the economy. Be clear about the equilibrium prices of output and inputs, the quantities of output and inputs.
11. j. In the long run equilibrium, calculate the total surplus of the economy.
12. k. Consider a specific government policy. Analyze the effect of the policy on long run equilibrium, and the welfare effect on each party in the economy, as well as the total welfare effect.
13. 2. Suppose that the output market is a monopoly and the input markets are still competitive.
14. a. Characterize the short run equilibrium for the economy. Be clear about the equilibrium prices of output and inputs, and the quantities of output and inputs.
15. b. Characterize the long run equilibrium for the economy, including the prices of output and inputs, the quantities of output and inputs.
16. c. In the long run equilibrium, calculate the total surplus of the economy.
17. d. Compare the long run equilibrium outcome and total surplus to that of the unregulated and perfectly competitive market. Calculate the deadweight loss.

Part III. Bonus Questions (20 points)

1. Suppose in Case 2 of Part II, the monopolist output producer can adopt two-part tariff.

a. Characterize the profit-maximizing two-part tariff. Be clear about the entry fee and the usage fee.

b. Solve the prices of inputs, and the quantities of output and inputs under the two-part tariff.

c. Calculate the total surplus under the two-part tariff.