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Econ 4351: Lecture 2 Practice Exam 2 Dr. Myoung Lee University of Missouri Name: SOLUTION Student Number: . Total Points earned: 110pts . ECON 4351: EXAM 2 SPRING, 2014 You have 75 minutes to answer the following questions. Directions: You should have nothing on your desk at this time other than the exam, pencils and an eraser. - Do not expect me to read your mind!!! The exam will be graded based ONLY on what you write in the space provided. - Please show your work (step by step) for every question in order to get full credit. Even correct answers will get zero points if you do not show your work. - Your handwriting must be legible, and you must make sure that I can follow your logic.Econ 4351: Lecture 2 Practice Exam 2 Dr. Myoung Lee University of Missouri 1. (2pt) Explain what is meant by the term “A firm’s isoquant.” Use words, not equations. The various combinations of capital and labor that will produce a given amount of output. 2. (2pt) Find the marginal product of capital for the production function, 212215 KKLQ . 21212110 KKLdKdQMPK 3. (12pt) Determine the type of returns to scale for the following production functions. (a) (4) ƒ 21, XX = 212XX  ƒ 212,2 XX = )2(2221XX …(2) 2ƒ 21, XX = 2(212XX )…(1) = 2142 XX  = 2(212XX ) => CRTS, ƒ 212,2 XX = 2ƒ 21, XX (b) (4) ƒ (L,K) = L2 + K½ F(2L, 2K) = (2L) 2 + (2K) ½…(1) 2F(L, K) = 2 (L2 + K½)…(1) = 22L2 + (2½ K½) = 2L2 + 2K½ => 22L2 > 2 L2 and (2½ K½) < 2K½…(2) => Don’t’ know (c) (4) ƒ 21, XX = 212XX  ƒ 212,2 XX =  21222 XX …(1) 2ƒ 21, XX = 2212XX …(1) = 2142 XX  = 2212XX   DRTS, ƒ 212,2 XX < 2ƒ 21, XX 4. (6pt) Define and prove that Producer Surplus is equal to Total revenue –Variable costs as shown in lecture. PS is Difference between Profit producing at optimal output, Q* and not producing output…(3) PS = π – (- FC) = π + FC = TR – TC + FC Need to show all steps……………………………………….(3) = TR - (FC+VC) + FC = TR – VC 5. (6pt) The production function for Widgets is given by 414116 KLQ . The price of labor (w) is $30 and the price of capital (r) is $30. (a) (2) What is MPL? 41434 KLdLdQMPL (b) (2) What is MPK? 43414 KLdKdQMPK (c) (2) What is APL? 414341411616KLLKLLQAPLEcon 4351: Lecture 2 Practice Exam 2 Dr. Myoung Lee University of Missouri 6. (8pt) The production function for Widgets is given by Q= 2 L2 K The price of labor (w) is $20 and the price of capital (r) is $40. How much labor and capital would be required to minimize the cost of producing 4,000 widgets? Cost minimizing (L*, K* ) must satisfies: .. ……………Need to state it to start 54*,20*10280002142400040002),(.24*4*402024020.1333322LKLLLLLQatKLQKLfQKLorLKLKMPMPrwMRTSKL 7. (16pt) You manage a plant that mass produces engines by teams of workers using assembly machines. The technology is summarized by the production function: q = 5 KL where q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r = $10,000 per week and each team costs w = $5,000 per week. Engine costs are given by the cost of labor teams and machines, plus $2,000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design, but rent must still be paid for these machines. (a) (6) What is the cost function for your plant — namely, how much would it cost to produce q engines? What are average and marginal costs for producing q engines? How do average costs vary with output? K is fixed at 5. The SR production fn is q = 25L. This implies that for any level of output q, the # of L teams hired will be L =q/25. The TC: qqqqwLrKqTC 200,2000,50000,225000,55000,102000)(  200,2)(arg;200,2000,50)( dqdTCqCostinalMqqTCqCostAverage MC is constant & AC decreases as q increases. (b) (4) How many teams are required to produce 250 engines? What is the average cost per engine? To produce q = 250 engines we need labor teams L=q/25 or L=10. Average costs are given by AC(q  250) 50,000  2200(250)250 2400. (c) (6) You are asked to make recommendations for the design of a new production facility. What capital/labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing any level of output q? Using production function, q = 5 KL. MPKQK 5L and MPLQL 5K Find the combination of K and L that minimizes costs at any level of output q: apply the equi-marginal principle, wMPrMPLK. Using the principle to minimize the cost: The new plant should accommodate a capital to labor ratio of 1 to 2. Note that the current firm is presently operating at this capital-labor ratio. LKLLKMPMPMRTSwhereKL224,2 Need to state it to star.N .Need to all steps ed tNeed to show the steps 5Lr5KwKLwr500010,00012Econ 4351: Lecture 2 Practice Exam 2 Dr. Myoung Lee University of Missouri 8. (14pt) Consider the following diagram where a perfectly competitive firm faces a price of $10. (a) (2) Identify AC, AVC, MC and MR curves on the graph. (b) (2) What is the capacity output of this firm? Q= 50 where MC= min AC (c) (2) What is the profit maximizing output? Q* =40 where P=MC (d) (1) What is the ATC at the profit maximizing level of output? $16 (e) (1) What is the AVC at the profit maximizing level of output? $10 (f) (2) What is the FC? AFCXQ= $6 X 40 = $240 (g) (2) What is total revenue and profit at the profit maximizing level of output? TR=$10X40=400, TC=16X40=640………. (1) Profit=TR-TC=400-640 = - 240…………… (1) (h) (2) What is shut down price? $10 20 15 11 10 6 4 16 13 10 20 30 40 50 60 70 80 90 19 MC AC AVC $ Q MREcon 4351: Lecture 2 Practice Exam 2 Dr. Myoung Lee


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