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Chapter 7 Exercises 1, 6, 8, and 9 and Chapter 8 2a, 4, and 6a

In: Business and Management

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Week 4 Check Your Understanding Exercises July 22, 2013

Chapter 7 – 1, 6, 8 and 9 1. In the Deep Creek Mining Company example described in this chapter (Table 7.1), suppose again that labor is the variable input and capital is the fixed input. Specifically, assume that the firm owns a piece of equipment having a 500-bhp rating. a. Complete the following table: LABOR INPUT L (NO. OF WORKERS) | TOTAL PRODUCT TPL (= Q) | MARGINAL PRODUCT MPL | AVERAGE PRODUCT APL | 1 | 3 | - | 3 | 2 | 6 | 3 | 2 | 3 | 16 | 10 | 5.33 | 4 | 29 | 13 | 7.25 | 5 | 43 | 14 | 8.6 | 6 | 55 | 12 | 9.16 | 7 | 58 | 3 | 8.28 | 8 | 60 | 2 | 7.5 | 9 | 59 | -1 | 6.5 | 10 | 56 | -3 | 5.6 | b. Plot the (i) total product, (ii) marginal product, and (iii) average product functions.

c. Determine the boundaries of the three stages of production. In Stage 1, both AP and MP are rising. MP Reaches its maximum point and starts falling. The point to note is that MP is always greater than AP in this stage. In stage 2, AP reaches its maximum point and starts falling. MP also falls and becomes zero. Here MP is always less than AP. In stage 3, MP becomes negative and AP decreases but remains positive.

6. Consider the following short-run production function (where L = variable input, Q = output): Q = 10L – 0.5L2 Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit. a. Determine the marginal revenue product function. MRPL = MPL x MR given P = AR = MR = 10 given MPL = dQ dL MPL = 10 – L MRPL = 100 – 10L b. Determine the marginal factor cost function. $20 c. Determine the optimal value of L, given that the objective is to maximize profits. MRPL = MFC...

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