Unformatted text preview: ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission University of Toronto, Department of Economics, ECO 204, 20082009. Ajaz Hussain Test 2 PLEASE FILL OUT THE INFORMATION BELOW Please write your name as it appears in ROSI: LAST NAME: FIRST NAME: MIDDLE NAME: UT ID #: SIGNATURE: PLEASE CIRCLE THE SECTION YOU'RE REGISTERED IN (NOT THE SECTION YOU'RE ATTENDING) M 122 M 46 T 122 T 46 W 68 PLEASE CIRCLE YOUR EXAM ROOM: EX 100 EX 310 EX 320 SCORES Question 1. 2. 3. 4. 5. 6. 7. Total Points 10 10 10 10 30 10 20 100 Score For your convenience there is a worksheet at the end of this test. This test has a total of 15 pages. Good luck! 1 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission Imperfect Substitutes Formulas: q = L K L = q1/( + ) [(/)(PK/PL)]/( + ) K = q1/( + ) [(/)(PL/PK)]/( + ) C(q) = q1/( + ) PL /( + ) PK/( + ) [(/) + (/)]1/( + ) __________________________________________________________________________ Question 1 (10 points) Edison Chang has the production function q = L K + L + K. Suppose Edison Chang is in the long run. Calculate Edison Chang's MRTS show all calculations clearly. 2 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission Question 2 (10 points) MazaMataHari has the production function q = L k. Suppose MazaMataHari is in the short run. What is MazaMataHari `s MRTS (in terms of q) at the fixed capital and optimal labor? Show all calculations clearly. 3 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission Question 3 (10 points) A company uses Labor (L), Capital (K) and Materials (M) as inputs to produce target output q with the production function q = L K M. (a) (5 points) For what values of , and will this company have constant returns to scale? Show your calculations below. (b) (5 points) For what values of , and will this company have decreasing returns with respect to materials? Show your calculations below. 4 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission Question 4 (10 points) A company uses Labor (L) and Capital (K) as inputs to produce target output q with the production function q = min(L, K) + . For what values of , and will this company have increasing returns to scale? Show your calculations below. 5 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission Question 5 (30 points) The Colgate Company manufactures toothbrushes using labor and capital as inputs in a complements technology q = min(K, L). Every 1m toothbrushes requires 1 capital and 1 labor. Each unit of Colgate's capital (K) consists of: 1 Tufter machine which inserts the brush into the handle 1 Handle Mold machine which produces the handle 1 Packaging machine which packages the toothbrush These machines are specifically designed for Colgate toothbrushes and cannot be used by other companies to manufacture any product. Table 1 has the purchase price and depreciation time: Table 1 Purchase Price $500,000 $300,000 $150,000 Machine Tufter Handle Mold Packaging Depreciation Time 15 years 5 years 5 years Source: ColgatePalmolive Company: The Precision Toothbrush, HBS Case 9593064 Suppose Colgate hires workers in competitive markets at PL = $10. Currently, the average interest rate for bank deposits is 5%. Colgate's target output is 2m toothbrushes a year. (a) (5 points) Use the straight line depreciation method to calculate the annual depreciation (up to two decimal places) for the Tufter, Handle Mold and Packaging machines. Show your calculations below. 6 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission (b) (5 points) Use the answer in part (a) to compute the annual depreciation for Colgate's capital. Hint: it's not constant over time. (c) (5 points) What is the annual opportunity cost of Colgate's capital? 7 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission (d) (5 points) Use your answers in parts (a), (b) and (c) to calculate Colgate's price of capital PK in Table 2 below: Table 2 Year PK 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (e) (5 points) Assuming wages and the target output of toothbrushes are constant, calculate Colgate's optimal labor and capital usage over time. Explain your answer using algebra and/or graphs. 8 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission (f) (5 points) Assuming that wages and the target output of toothbrushes are constant calculate Colgate's total costs in Table 3 below. Show all calculations below. Table 3 Year C(q) 1 3 5 7 10 9 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission Question 6 (10 points) ETorre Enterprises used labor (L) and capital (K) to produce its target output q = 80 according to the production function q = L + K where = 2 and = 8. ETorre procures labor and leases capital in competitive markets. Currently, PL = $100 and PK = $10. (a) (5 points) If ETorre is in the long run, how much labor and capital does it use? Show your calculations below. 10 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission (b) (5 points) Plot your answer to part (a) in Figure 1 below. Now suppose PL decreases: graph the resulting demand curve for labor in Figure 1 below: Figure 1 11 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission Question 7 (20 points) The following page contains Exhibits 1 and 2 from the Prestige Telephone Company case, as well as Exhibit 3 from the solution. Recall Pcommercial = $800/hr and Pintercompany = $400/hr. (a) (10 points) Suppose Prestige Data Services raises commercial prices to $1,200/hr. Higher commercial prices will lead to lower commercial sales. What must the new number of commercial hours be for Prestige Data Services to be profitable? Show all calculations. 12 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission (b) (10 points) Suppose Prestige Data Services spends $7,720 on sales promotion (i.e. advertising). Assuming advertising raises sales of commercial hours, calculate the increase in commercial hours needed to make Prestige Data Services profitable. Show all calculations. The End 13 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission Exhibit 1 Prestige Data Services Summary of Computer Utilization, First Quarter 2003 Revenue Hours Intercompany Commercial Total revenue hours Service hours Available hours Total hours January 206 123 329 32 199 560 February 181 135 316 32 164 512 March 223 138 361 40 143 544 Exhibit 2 Prestige Data Services Summary Results of Operations, First Quarter 2003 January Revenues Intercompany sales Commercial sales Computer use Other Total Revenue Expenses Space costs Rent Custodial services February March $ 82,400 98,400 9,241 190,041 $ 72,400 108,000 9,184 189,584 $ 89,200 110,400 12,685 212,285 $ 8,000 1,240 9,240 $ 8,000 1,240 9,240 $ 8,000 1,240 9,240 Equipment costs Computer leases Maintenance Depreciation: Computer equipment Office equipment and fixtures Power 95,000 5,400 25,500 680 1,633 128,213 95,000 5,400 25,500 680 1,592 128,172 95,000 5,400 25,500 680 1,803 128,383 Wages and salaries Operations Systems development and maintenance Administration Sales 29,496 12,000 9,000 11,200 61,696 9,031 7,909 15,424 $ 231,513 $ (41,472) 29,184 12,000 9,000 11,200 61,384 8,731 7,039 15,359 $ 229,925 $ (40,341) 30,264 12,000 9,000 11,200 62,464 10,317 8,083 15,236 $ 233,723 $ (21,438) Materials Sales promotions Corporate services Total expenses Net income/(loss) Exhibit 3 Prestige Data Services Standard Costs  Average Month, First Quarter 2003 Variable Costs Power per hour Operations wages Total variable expenses per hour Fixed Costs Rent Custodial Computer lease Computer maintenance Depreciation Power Wages and Salaries Operations Systems development Administration Sales $4 $24 $28 $8,000 $1,240 $95,000 $5,400 $26,180 $200 $21,600 $12,000 $9,000 $11,200 Total Wages & Salaries Fixed Costs $53,800 Total nonvariable expenses Sales promotion $189,820 $8,000 $197,820 << Total Fixed Costs 14 ECO 204, 20082009, Test 2 This test is copyright material and may not be used for commercial purposes without prior permission WORKSHEET 15 ...
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