Answers to Homework # 4

Answers to Homework # 4 1) The following table represents an annual production function for corn. The first column indicates the amount of land used (acres per year) and the first row indicates the amount of labor used (number of workers per year). 1 2 3 4 5 6 1 50 150 275 375 450 500 2 150 370 550 700 825 900 3 240 500 740 940 1080 1160 4 300 660 920 1060 1190 1270 5 330 790 1050 1160 1250 1320 6 340 900 1050 1250 1300 1330 a. Using the above production function, calculate total output, the average physical product of labor (APPL), and the marginal physical product of labor (MPPL) when the amount of land is fixed at 3 acres. To answer this question, recall that average physical product = total output/input quantity; and marginal physical product = change in total output when the input is increased by 1 unit. Acres Workers Total Output APPL MPPL 3 1 240 240 240 3 2 500 250 260 3 3 740 246.7 240 3 4 940 235 200 3 5 1080 216 140 3 6 1160 193.3 80 b. Suppose the farmer uses 1 worker and 1 acre of land. Over time, he expands production by increasing the use of both inputs proportionately. Does the farmer experience increasing, constant, or decreasing returns to scale as he expands? Both inputs are increasing proportionately along the diagonal. Returns to scale increase then decrease in this production function. Decreasing returns to scale set in after 4 workers and 4 acres are hired. When both inputs are increased from 4 to 5 units, input usage has increased by 25%, yet output increased by only 18%. 1 c. If the amount of land is held fixed at 3 acres, when do diminishing marginal returns for labor set in? Diminishing marginal returns set in after the second worker is hired. 2) You are currently going to college. Consider yourself to be a "firm" utilizing inputs to produce an output. What is the output? What are the inputs you use to produce the output? Describe a situation when diminishing marginal returns applies. Output could be defined as knowledge gained by going to college or by the diploma. Inputs include the faculty, classrooms, paper, books, the library, computers, land the college is on, as well as you. Diminishing marginal returns would apply whenever you try to increase your rate of output without increasing all inputs proportionately. For example, attending class more frequently while holding the number of hours spent studying constant. 3) Starbucks finds that as it increases the number of workers it hires, the number of mochas produced weekly changes as follows: Workers Mochas MPPL MRPL (P = $3) MRPL (P = $4) 1 100 100 300 400 2 300 200 600 800 3 600 300 900 1200 4 1000 400 1200 1600 5 1350 350 1050 1400 6 1650 300 900 1200 7 1900 250 750 1000 8 2100 200 600 800 9 2250 150 450 600 10 2350 100 300 400 11 2400 50 150 200 12 2400 0 0 0 13 2350 -50 -150 -200 a. The price of mochas can be $3 or $4 each. For each number of workers, calculate the marginal physical product of labor (MPPL) and the two marginal revenue products of labor (MRPL) corresponding to the two mocha prices. Recall that MRPL = Product price x MPPL. The answers are provided in the table above. 2 b. Plot the MPPL curve and indicate the phases of increasing returns to labor, diminishing returns, and negative returns. MPPL rises from 1 to 4 workers; falls from 4 to 12 workers; and becomes negative once the 13th worker is hired. c. Assume the price of mochas is $3. If the wage rate of labor is $600 a week, how many workers will Starbucks hire? Note: there are 2 employment levels at which the wage equals the MRPL. Explain why you picked one and not the other. Wage = MRPL at 2 and 8 workers. Profits are maximized by hiring 8 workers. The firms profits are lower if only 2 workers are hired. Each worker from 3 to 7 generates additional profits, because revenues (MRPL) exceed the cost of labor (wage). Note: the 2nd and 8th workers are hired even though the firm earns zero profits from these workers. Both workers are worth (MRPL) their wage to the firm. Also, the firm loses money by hiring the 1st worker (MRPL < wage) yet, does so, in order to hire the next 7 workers. d. When the wage falls to $400, what will the new employment level be? Carefully explain why the next worker is not hired. Starbucks will hire 9 workers where the MRPL > wage. The 10th worker is not hired, because the $400 cost of hiring the worker exceeds the $300 in revenue that is generated by the worker. Starbucks would lose $100 by hiring the 10th worker. e. How does the employment change when the price of mochas rises from $3 to $4, if the wage rate remains at $400? The increased product price raises the MRPL and thereby raises the demand for labor. Starbucks will now hire 10 workers instead of 9. 3