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 1 2pt Explain what is meant by the term A firm s isoquant Use words not equations Practice Exam 2 The various combinations of capital and labor that will produce a given amount of output Dr Myoung Lee University of Missouri a 4 2 2pt Find the marginal product of capital for the production function 3 12pt Determine the type of returns to scale for the following production functions 2 CRTS 2 2 2 2 1 2L 2 2K 1 22L2 2 K 22L2 2 L2 and 2 K 2K 2 Don t know 2F L K 2 L2 K 1 2L2 2K b 4 L K L2 K F 2L 2K c 4 DRTS 2 1 2 2 1 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 FC 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 The price of labor w is 30 and the price of capital r is 30 a 2 What is MPL b 2 What is MPK c 2 What is APL 212215KKLQ 21212110 KKLdKdQMPK 21 XX212XX 212 2XX 2 2221XX 21 XX212XX 2142XX 212XX 212 2XX 21 XX 21 XX212XX 212 2XX 21222XX 21 XX212XX 2142XX 2212XX 212 2XX 21 XX414116KLQ 41434KLdLdQMPL 43414 KLdKdQMPK414341411616KLLKLLQAPL Cost minimizing L K must satisfies Need to state it to start Econ 4351 Lecture 2 6 8pt The production function for Widgets is given by Q 2 L2 K Practice Exam 2 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 Dr Myoung Lee University of Missouri Need to show the steps 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 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 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 Find the combination of K and L that minimizes costs at any level of output q apply the equi marginal principle 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 N e e d t o s t a t e i t t o s t a r N e e d t o a l l s t e p s e d t N 54 20 10280002142400040002 24 4 402024020 1333322 LKLLLLLQatKLQKLfQKLorLKLKMPMPrwMRTSKLqqqqwLrKqTC200 2000 50000 225000 55000 102000 200 2 arg 200 2000 50 dqdTCqCostinalMqqTCqCostAverage AC q 250 50 000 2200 250 250 2400 MPK Q K 5L and MPL Q L 5KwMPrMPLK LKLLKMPMPMRTSwhereKL224 2 5Lr 5Kw KL wr 500010 000 12 Econ 4351 Lecture 2 8 14pt Consider the following diagram where a perfectly competitive firm faces a price of 10 Practice Exam 2 Dr Myoung Lee University of Missouri MC AC AVC MR Q 15 20 13 19 16 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 11 10 6 4 c 2 What is the profit maximizing output Q 40 where P MC 10 20 30 40 50 60 70 80 90 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 Econ 4351 Lecture 2 Practice Exam 2 9 20pt A firm has the following short run cost function a 5 What is the fixed cost and variable cost Dr Myoung Lee University of Missouri Derive an equation for this firm s average cost average variable cost and marginal cost functions b 3 Sketch the and the curves c 4 Shade in profits if the price of output is 24 you do not have to calculate profits curves on the axis provided below Denote the slopes of the and d 4 Assume there are n firms with the same cost function operating in a competitive industry with free entry Derive an expression for the industry supply curve Hint what is the individual firm supply curve e 4 If the demand curve for this product is what is the equilibrium number of firms in this industry if the price is 20 5022 qqTC50 22 FCqVC qqqqqqcqAC5025022 qqqqqVCqAVC22 2 qqqcqMC4 qAC qAVC qMC qAVC qMC2055052 5 52550245024502 …