# Economics 105 Burhan Biner DePaul University Winter 2016 Problem Set II Due March 2, in class. As long as your handwriting is legible you can write…

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Suppose that the demand curve for apartments near the university isgiven byP = 1000 − Qand the supply curve is given byP = 400 + 2Qa. (4) Plot a diagram of the market for apartments. b. (4) Find the equilibrium in the market.c. (4) Find the consumer surplus, the producer surplus and the total surplus fromthe market.d. (4) Suppose that the local government, in an attempt to help the studentsfinancially, imposes a price ceiling of $500 on rental apartments. Find thenumber of apartments that students will be able to rent at that price.e. (4) Find the excess demand for rental apartments that will arise from the priceceiling.f. (4) Find the consumer surplus, the producer surplus, the total surplus and thedeadweight loss in the presence of the price ceiling.g. (4) Illustrate with a diagram the market for apartments after the price ceiling isimposed and show on your diagram the excess demand in the market, theconsumer surplus, the producer surplus, and the deadweight loss resultingfrom the price ceiling.2. (10 Points) Suppose that Micronesia is a small country that imports milk (thus, ittakes the world price of milk as given). Illustrate with the help of a diagram theeffects of a price subsidy of $x for milk. On your diagram show the consumersurplus before and after the price subsidy as well as the deadweight loss resultingfrom the price subsidy.3. (16 Points) The following claim is often made with respect to per unit taxesimposed on some good or service: “the producers will pass the tax to theconsumers”.a. (4) Show a diagram of a market after a tax of $T is imposed on a good andillustrate that the tax burden is shared between the consumers and theproducers. In your graph label the burden on the consumer and the burden onthe producer as a result of the tax.b. (4) What determines who pays larger fraction of the tax, the sellers or thebuyers? Explain with the use of a diagram.c. (4) Show on the same diagram in part b the deadweight loss that results fromthe tax. 2 d. (4) The deadweight loss due to a tax is smaller, the more elastic the demandcurve for that good is. True/false, explain with the help of a diagram.4. (16 Points) Illustrate with the help of a diagram the effects of a tariff imposed onan imported good. On your diagram, illustrate the deadweight loss resulting fromthe tariff.5. (30 Points) Suppose that the capital (machines) in a particular plant is fixed inthe short run and is equal to K = 2. Thus the only way to change the output levelis by changing the number of workers (L). The technology of the firm (in theshort run) is described in the following table.K22222222222 L012345678910 Q0100220340450550640720790850900 MPL a. Calculate the Marginal Product of Labor (MPL) in the above table andplot the graphs of output (Q) and MPL as functions of labor (L) on thesame diagram.b. Does the law of diminishing marginal product hold for this technology?Explain.c. Complete the costs in the following table, assuming thatPK = 30, PL = 100 .d. (Excel required). Plot the graphs of ATC, AVC, and MC on the samediagram.e. Calculate the profit of the firm for the following market prices:PX = $1, PX = $1.25, PX = $2 .f. Show the firm’s profit when the price is $1.25 on the diagram in section d.g. For each of the given above market prices, state whether the firm willoperate in the short run? In the long run? 3

Economics 105 Burhan Biner DePaul University Winter 2016 Problem Set II Due March 2, in class. As long as your handwriting is legible you can write…

1 Economics 105 DePaul University Burhan Biner Winter 2016 Problem Set II Due March 2, in class. Before you begin writing your answers make sure that you read and fully understand the assignment rules. As long as your handwriting is legible you can write your homework rather than type . Assignment rules: 1. Homework assignments must be submitted at the end of the lecture, in class, on the due date. 2. Late homework assignments will not be accepted under any circumstances. 3. Submitted assignments must be stapled. Non-stapled assignments will receive a maximum grade of 80%. A non-stapled homework will be graded as normal and then the grade will be multiplied by 80%. 4. Your answers must be numbered and must be presented in a neat and orderly fashion. This means that the answers must be ordered in the same order as the questions and within each question, the sections must appear in the alphabetical order. You are required to place the entire answer for a question or a section within that section. For example, if the answer to section d of question 3 contains some verbal answer as well as a graph, then both the verbal answer and the graph must appear together in your answer to section d of question 3. You cannot provide the verbal answer and write, “see the attached graph”. I instructed the Grader to give a maximum of 80% to an assignment in which the answers are in the wrong order. In an extreme case, if the submitted assignment is not comprehensible and the graders cannot figure out which answer corresponds to which question, the assignment will receive the grade of 0%. 5. Assignments must be typed, except graphs and formulas or they will receive a maximum grade of 80%. Otherwise, the homework will be graded as normal and then the grade will be multiplied by 80%. 6. In all of the questions you are required to show the way you got to the solution. Presenting only the final answer, without showing your work will result in zero points for that question, even if the answer is correct. 7. Only those graphs that I ask to plot with Excel need to be plotted with Excel. Other graphs can be drawn either with pencil or using Excel. 8. You are encouraged to collaborate on the homework assignments, but submitted work must be your own. This means that you should write your answers independently. On each assignment you are required to note the names of your collaborators. NOTE: Turning in identical homework assignments will result in a zero for both parties. 2 1. (28 Points) Suppose that the demand curve for apartments near the university is given by Q P− =1000 and the supply curve is given by Q P2 400 + = = a. (4) Plot a diagram of the market for apartments. b. (4) Find the equilibrium in the market. c. (4) Find the consumer surplus, the producer surplus and the total surplus from the market. d. (4) Suppose that the local government, in an attempt to help the students financially, imposes a price ceiling of $500 on rental apartments. Find the number of apartments that students will be able to rent at that price. e. (4) Find the excess demand for rental apartments that will arise from the price ceiling. f. (4) Find the consumer surplus, the producer surplus, the total surplus and the deadweight loss in the presence of the price ceiling. g. (4) Illustrate with a diagram the market for apartments after the price ceiling is imposed and show on your diagram the excess demand in the market, the consumer surplus, the producer surplus, and the deadweight loss resulting from the price ceiling. 2. (10 Points) Suppose that Micronesia is a small country that imports milk (thus, it takes the world price of milk as given). Illustrate with the help of a diagram the effects of a price subsidy of $x for milk. On your diagram show the consumer surplus before and after the price subsidy as well as the deadweight loss resulting from the price subsidy. 3. (16 Points) The following claim is often made with respect to per unit taxes imposed on some good or service: “the producers will pass the tax to the consumers”. a. (4) Show a diagram of a market after a tax of $T is imposed on a good and illustrate that the tax burden is shared between the consumers and the producers. In your graph label the burden on the consumer and the burden on the producer as a result of the tax. b. (4) What determines who pays larger fraction of the tax, the sellers or the buyers? Explain with the use of a diagram. c. (4) Show on the same diagram in part b the deadweight loss that results from the tax. 3 d. (4) The deadweight loss due to a tax is smaller, the more elastic the demand curve for that good is. True/false, explain with the help of a diagram. 4. (16 Points) Illustrate with the help of a diagram the effects of a tariff imposed on an imported good. On your diagram, illustrate the deadweight loss resulting from the tariff. 5. (30 Points) Suppose that the capital (machines) in a particular plant is fixed in the short run and is equal to K = 2. Thus the only way to change the output level is by changing the number of workers (L). The technology of the firm (in the short run) is described in the following table. K L Q MPL 2 0 0 2 1 100 2 2 220 2 3 340 2 4 450 2 5 550 2 6 640 2 7 720 2 8 790 2 9 850 2 10 900 a. Calculate the Marginal Product of Labor (MPL) in the above table and plot the graphs of output (Q) and MPL as functions of labor (L) on the same diagram. b. Does the law of diminishing marginal product hold for this technology? Explain. c. Complete the costs in the following table, assuming that 100 , 30= = L KP P . d. (Excel required). Plot the graphs of ATC, AVC, and MC on the same diagram. e. Calculate the profit of the firm for the following market prices: 2 $ , 25 . 1 $ , 1 $ = = = X X XP P P . f. Show the firm’s profit when the price is $1.25 on the diagram in section d. g. For each of the given above market prices, state whether the firm will operate in the short run? In the long run?

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