Imagine you own a business firm all by yourself. During the first quarter of your production, you come up with the following information that: 2. • Output Elasticity of Capital (x) is 0.45 • Output Elasticity of Labour (y) is 0.55 • Total Factor Productivity is 10 (i) What kind of business firm is the one that you own? Mention 2 of its characteristics. (ii) Derive the marginal productivity of capital and labour, by means of Cobb- Douglas production function. (iii) If Y = F (K, L) where K = 1000 and L = 400, calculate the values of MPK and %3D MPL. (2 + 4 + 4 = 10 marks)

Imagine you own a business firm all by yourself. During the first quarter of your production, you come up with the following information that: 2. • Output Elasticity of Capital (x) is 0.45 • Output Elasticity of Labour (y) is 0.55 • Total Factor Productivity is 10 (i) What kind of business firm is the one that you own? Mention 2 of its characteristics. (ii) Derive the marginal productivity of capital and labour, by means of Cobb- Douglas production function. (iii) If Y = F (K, L) where K = 1000 and L = 400, calculate the values of MPK and %3D MPL. (2 + 4 + 4 = 10 marks)

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter7: Production And Cost In The Firm

Section: Chapter Questions

Problem 18PAE

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2. The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3K1/3, where P is the number of anvils produced when L is the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. c. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. Only need paVAS e and fl
Question 8 of 13 The following diagram depicts the production function of the farmers, where diminishing average product of labour is assumed. At A the average product of labour is 500,000/800 = 625 kg of grain per farmer. At B the average product of labour is 732,000/1,600 = 458 kg of grain per farmer. If you know that for 2,800 farmers the grain output is 894,000kg, then which of the following is/are correct? Kilogrammes of grain produced (thousands) 900 800- 700- 600- 500 400- 300- 200- 100- 0 0 400 800 B 1,200 1,600 Number of farmers 2,000 2,400 2,800 OA. The average product of labour when the labour input is 2,800 is 300. OB. The decreasing slopes of the rays from the origin to the production function along the curve indicate the decreasing average product of labour. OC. If the production function curve is an upward-sloping straight line, then there is no diminishing average product of labour. OD. It is possible that initially there is an economy of scale: for example, going from…
Exercise 11 Question Help Suppose that a firm's production function is: 112- q = 10L0.5K0.5 98- Its marginal product functions are: 84- MP, = 5KO.5/L0.5 - 0.5g/L 70- and MPK = 5L0.5/K.5 - 0.5g/K. 56- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. 42- 28- Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. 14- -q= 280 q= 140 98 Suppose now that the firm wants to increase output to 280 units. If capital is fixed 0- in the short run, how much labor will the firm require? 70 84 L, Units of labor 14 28 42 56 112 The firm will now require units of labor. (Enter your response rounded to two decimal places.) K, Units of capital
The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1
A firm uses the inputs of Iron and labor to produce Cars. Suppose that the quantity of labor is fixed. The quantity of Iron and the number of Cars produced is given by the following table: Tons of Iron per week Number of Cars per week 0 0 10 50 20 100 30 170 40 220 50 250 60 260 70 250 80 200 What is the average product of Iron when 40 tons are used? What is the marginal product of the 60th ton Iron? Does this production function exhibit diminishing marginal returns? If so, at what quantity of Iron do they start to occur?
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3. The Chipper Cookie Company's output is given by the Cobb-Douglas Production function P = 120L0.7 K0.3, where P is the number of units produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 600 and K = 600? b. Find the marginal productivities. c. Evaluate the marginal productivities with L= 600 and K = 600. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $1200 then there is a constraint L+ K = 1200. Use Lagrange multipliers (^) to find the values of L and K that will maximize production and find the maximum production f. Find and interpret 2 for this problem. only need part e and f!