Demand functionQA=75-PQB=25-4P500 identical consumers with each following individual demand functionMarket Demand: Q= 500(QA+QB) =500(75-P + 25-4P)= 500(100-5P)= 5000-2500PProduction Function: Q (L,K) =0.5L^0.5K^21. Suppose that all markets are competitive with one representative firm in the output market.a. Derive the market demand for the output.b. Draw an isoquant curve for the output by connecting multiple input combinations.c. Derive the marginal rate of technical substitution (MRTS) from the production function.d. Given the input prices, and , express and draw the isocost line.e. Derive the total cost function of output for both short run and long run.f. Derive the marginal cost and average cost for both short run and long run.g. Derive the supply curve of output for both short run and long run.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.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.j. In the long run equilibrium, calculate the total surplus of the economy.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.2. Suppose that the output market is a monopoly and the input markets are still competitive.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.b. Characterize the long run equilibrium for the economy, including the prices of output and inputs, the quantities of output and inputs.c. In the long run equilibrium, calculate the total surplus of the economy.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.

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

Microeconomics Spring 2020 Final Project Due: July 3rd 17:00 In th e final projec t, you should finish the following two parts which account for 100 points in total. There is also a bonus part which accounts for 20 points. Your final project should be in English with 12 -point font size and 1.5 line space, and should be submitted in a pdf file. Whereas you can use calculator or computer software to obtain numerical results, you should be clear about each step of your analysi s. The evaluation of your final project will depend on the clarity and novelty of your model, and the accuracy and completeness of your analysis. You should work on the project on your ow n. Any form of cheating or plagiarism will result in a fail of your final gr ade of this course . Part I . Consumer Theory and General Equilibrium (40 points) I. Model 1. Specify two goods. For example: food F and clothing C 2. Specify two consumers’ utility functions. For example: 1(,)= 0.50.5, 2(,)= 0.40.6. II. Analysis 1. For each consumer , = 1,2, solve the following problems . a. Draw an indifference curve by connecting multiple consumption bundles. b. Derive the marginal rate of substitution ( MRS ) from the utility function. c. Given the prices, , , and the income , express and dr aw the budget constraint. d. Solve the optimal consumption bundle as functions of , , and . e. Derive and draw the individual demand curve for each good. f. Illustrate the substitution and income effect for each good caused b y an increase in own price . 2. Consider a pure exchange economy between consumers 1 and 2 with the above two goods . a. Draw the Edgeworth box, and specify each consumer’s endowment of each good. b. Show whether the endowment point is Pareto efficient or not. If not, show the area where there can be mutually beneficial trade with respect to the endowment point . c. Derive and draw the contract curve in the Edgeworth box . d. Suppose the economy is in a competitive equilibrium , solve the equilibrium consumption bundles as functions of the price ratio and total endowments . e. Characterize the competitive equilibrium starting from the endowment point . Be clear about the equilibrium consumptions, the price ratios, and the consumers’ utility levels. Part II . Producer Theory and General Equilibrium (60 points) I. Model 1. Specify an output . For example: smar t phone . 2. Specify the demand functions for two different groups of consumers . For example: = 100 − , = 50 − 2. Also specify the number of consumers in each group. 3. Specify the production function for the output. For example: (,)= 0.250.25, 4. Specify the fixed cost to produce the output for both short run and long run. Explain the sources of the fixed costs if any. 5. Specify the short run supply of each input. For example: = 100 , = 10 ≤ 10 Explain why you assume the short run supply functions as they are. 6. Specify the long run supply of each input. For example: = 100 , = 10 . Explain why you assume the long run supply functions as they are. II. Analysis 1. Suppose that all markets are competitive with one representative firm in the output market . a. Derive the market demand for the output. b. Draw an isoquant curve for the output by connecting multiple input combinations. c. Derive the marginal rate of technical substitution (MRTS) from the production function. d. Given the input prices, and , express and dr aw the isocost line. e. Derive the total cost function of output for both short run and long run . f. Derive the marginal cost and average cost for both short run and long run. g. Derive the supply curve of output for both short run and long run. h. Characterize the short run competiti ve equilibrium for the economy . Be clear about the equilibrium prices of output and inputs, the quantities of output and inputs. 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. j. In the long run equilibrium, calculate the total surplus of the economy . 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 we lfare effect . 2. Suppose that the output market is a monopoly and the input market s are still competitive. 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. b. Characterize the long run equilibrium for the economy, including the prices of output and inputs, the quantities of output and inputs. c. In the long run equilibrium, calculate the total surplus of the ec onomy. d. Compare the long run equilibrium outcome and total surplus to that of the unregulated and perfect ly 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 an d inputs under the two -part tariff. c. Calculate the total surplus under the two -part tariff.

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