12. A firm uses capital and labour to produce widgets. In the short-run capital is fixed, while labour is variable. The short-run production function is X-L'+24L +240L Where X is the number of widgets produced in per week, and L is the number of workers employed. Each worker works a 40-hour week. The wage rate is $12 per hour. a. Calculate the range of values for L over which the firm is in stage I, stage Il and stage II b. what is the minimum product price at which the firm will operate in the short-run? c. The product price, over which the firm has no control, is such that the firm's maximum possible pure profit $ 1096 per week. In order to achieve that level of profit it must employ 16 workers. How much is the firm's total fixed cost?.

12. A firm uses capital and labour to produce widgets. In the short-run capital is fixed, while labour is variable. The short-run production function is X-L'+24L +240L Where X is the number of widgets produced in per week, and L is the number of workers employed. Each worker works a 40-hour week. The wage rate is $12 per hour. a. Calculate the range of values for L over which the firm is in stage I, stage Il and stage II b. what is the minimum product price at which the firm will operate in the short-run? c. The product price, over which the firm has no control, is such that the firm's maximum possible pure profit $ 1096 per week. In order to achieve that level of profit it must employ 16 workers. How much is the firm's total fixed cost?.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

12. A firm uses capital and labour to produce widgets. In the short-run capital is fixed,
while labour is variable. The short-run production function is
X-L'+ 24L2+ 240L
Where X is the number of widgets produced in per week, and L is the number of workers
employed. Each worker works a 40-hour week. The wage rate is $12 per hour.
a. Calculate the range of values for L over which the firm is in stage I, stage II and stage
II
b. what is the minimum product price at which the firm will operate in the short-run?
c. The product price, over which the firm has no control, is such that the firm's
maximum possible pure profit $ 1096 per week. In order to achieve that level of profit it
must employ 16 workers. How much is the firm's total fixed cost?.

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3. A cost minimizing firm with q = K¹/21/2 that produces q = 40 pays w = 8 and r = 2. a. Provide an Isoquant and Isocost Diagram to illustrate and quantify this firm's choices for capital and labour as Bundle A. b. Next month the firm will reduce output to q = 20. In the short-run, Bundle B, the firm cannot change capital. In the long run, Bundle C, both capital and labour are variable. Update your diagram with calculated values for Bundles B and C.
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(a) Why does the labour demand curve slope downwards? (b) A garment factory’s production function is provided in the table.The gross profit per unit (difference between selling price and material cost, but not including the cost of labour) is $100. # Workers Output 1 20 2 36 3 48 4 56 5 60 6 62 (i) If the wage rate is $1,000 a week, how many workers should the factory hire? (ii) If a surge in popularity for the factory’s brand allows them to raise the product price such that the gross profit rises to $150, how many workers will the factory hire now? (iii) Calculate the number of garments produced in each of the two cases above.
(1) Let's go back to the beginning. q = AL^aK^1-a Suppose labor is fixed at some level L, a = 0.5, and A = 1. Calculate K* a)What is T C* ? b)What is the short-run fixed cost?
Suppose you are considering hiring another worker. Also assume that you are at a firm that is operating at a point where the marginal product of labor is 5 and the price of each unit of labor is $2, and the marginal product of capital is 20 and the price of each unit of capital is $10. Should you hire another worker? If you hire another worker, what will happen to the marginal product of labor and why?
(a) Why does the labour demand curve slope downwards? (b) A garment factory’s production function is provided in the table.The gross profit per unit (difference between selling price and material cost, but not including the cost of labour) is $100. # Workers Output 1 20 2 36 3 48 4 56 5 60 6 62 (i) If the wage rate is $1,000 a week, how many workers should the factory hire? (ii) If a surge in popularity for the factory’s brand allows them to raise the product price such that the gross profit rises to $150, how many workers will the factory hire now? (iii) Calculate the number of garments produced in each of the two cases above.
Exercise: If the fixed Input capital Is K* = 3 and the variable input of labor is from 0 by 2's to 20; and output Is from 0 for 0 labor, 76 for 2 laborers – from 76 Increase for every 25% of output starting for 4 laborers to 20 laborers. Find the change in labor, output, marginal product of labor and average product of labor. Show it in a table. Number of Labor (L) (1) (2) DL Change in Labor (3) (4) Total product or Output (Q) (5) (6) Average product (AP=Q/L) (8) Marginal product (MP-=DQ/DL) (9) (10)
14. A firm uses labour, L and capital K, to produce a single product, X. capital is fixed but labour is variable. The firm's production function is: X=-0.2L + 18L? + 1620L. Where X is the number of units of the product per week, and L is the number of persons employed. A. At what weekly output is marginal cost equal to average variable cost? B. if the price of the product is $0.20 per unit, what is the maximum weekly wage that the firm would pay rather than close down?
10. If over the range of positive marginal product, the short-run total product of factor A in the production of X is given by the equation: X=aA +b A2 – A3 Where a, and b are positive constants, and if the average product of A is maximized when X=100, then the marginal product of A must be greater than the average product when X=50. True or False ?. Prove your answer.
Assuming the firm is minimizing its cost and the price of labour is $10 per unit and the price of capital is $20 per unit. the marginal product of labour is 50, what must the marginal product of capital be?
. In the short run, labor is a hat-making firm’s only variable input. Wage rate is $5.00/hour. The firm currently employs a certain amount of labor H (hours), such that the marginal product of labor is 10 hats per worker-hour, and average product is 15 hats per worker-hour. MPL(H) = 10; APL(H) = 15. (Note: marginal and average products of labor for this firm are not constant. 10 and 15 are their values at a particular point, H, not everywhere.) What is the marginal cost of a hat for that firm?