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Lecture

Answers to Assignment Five.doc

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Department
Economics
Course
ECN 104
Professor
Tom Barbiero
Semester
Winter

Description
Answers to Assignment Five 1. Complete the following table by finding the average and marginal product. At what input-output level will average variable cost begin to rise? Explain. Inputs of Total Average Marginal labour product product product 0 0 _____ 1 8 _____ _____ 2 18 _____ _____ 3 25 _____ _____ 4 30 _____ _____ 5 33 _____ _____ 6 34 _____ _____ Inputs of Total Average Marginal labour product product product 0 0 0 1 8 8 8 2 18 9 10 3 25 8.33 7 4 30 7.50 5 5 33 6.60 3 6 34 5.67 1 With equal pay for each worker, average variable cost will begin to rise for the third worker’s output because that is the point where diminishing returns begin. 2. The table below shows the total production of a firm as the quantity of labour employed increases. The quantities of all other resources employed are constant. Compute the marginal and average products and enter them in the table. Marginal Average Units Total product product of Labour product of labour of labour 0 0 ––– ––– 1 40 ______ ______ 2 100 ______ ______ 3 165 ______ ______ 4 200 ______ ______ 5 225 ______ ______ 6 240 ______ ______ 7 245 ______ ______ 8 240 ______ ______ (a) At what levels are there increasing returns to labour and at what levels are there decreasing returns to labour? (b) Describe the relationship between the total product and marginal product. (c) Describe the relationship between marginal and average product. Marginal Average Units Total product product of Labour product of labour of labour 0 0 1 40 40 40 2 100 60 50 3 165 65 55 4 200 35 50 5 225 25 45 6 240 15 40 7 245 5 35 8 240 –5 30 (a) There are increasing returns to labour through the third worker hired. Decreasing returns to labour set in with the fourth worker. (b) Where total product increases at an increasing rate, marginal product rises (from 0 to 65). Where total product is increasing at a decreasing rate, marginal product is positive but falling (from 65 to 5). Where total product declines, marginal product is negative from 5 to –5. (c) Where marginal product is greater than average product, average product will rise. Where marginal product is less than average product, average product will fall. Marginal product intersects average product at maximum average product. 3. Assume that a firm has a plant of fixed size and that it can vary its output only by varying the amount of labour it employs. The table below shows the relationships between the amount of labour employed, the output of the firm, the marginal product of labour, and the average product of labour. (a) Assume each unit of labour costs the firm $20. Compute the total cost of labour for each quantity of labour the firm might employ, and enter these figures in the table. (b) Now determine the marginal cost of the firm’s product as the firm increases its output. Enter these figures in the table. (c) If labour is the only variable input, the total labour cost and total variable cost are equal. Find the average variable cost of the firm’s product. Enter these figures in the table. (d) Describe the relationship between the marginal product of labour and the marginal cost of the firm’s product. (e) Describe the relationship between the average product of labour and the average variable cost. Quantity Marginal Average Total Average of labour Total product product variable Marginal variable employed output of labour of labour cost cost cost 0 0 ––– ––– ––– ––– 1 10 10 10.00 $_____ $_____ $_____ 2 22 12 11.00 _____ _____ _____ 3 36 14 12.00 _____ _____ _____ 4 48 12 12.00 _____ _____ _____ 5 58 10 11.60 _____ _____ _____ 6 66 8 11.00 _____ _____ _____ 7 72 6 10.28 _____ _____ _____ 8 76 4 9.50 _____ _____ _____ 9 78 2 8.66 _____ _____ _____ 10 78 0 7.80 _____ _____ _____ Quantity Marginal Average Total Average of labour Total product product variable Marginal variable employed output of labour of labour cost cost cost 0 0 ––– ––– ––– ––– 1 10 10 10.00 $ 20 $2.00 $2.00 2 22 12 11.00 40 1.67 1.82 3 36 14 12.00 60 1.43 1.67 4 48 12 12.00 80 1.67 1.67 5 58 10 11.60 100 2.00 1.72 6 66  8 11.00 120 2.50 1.82 7 72  6 10.28 140 3.33 1.94 8 76  4  9.50 160 5.00 2.10 9 78  2
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