a. A firm has the production function X =L^1/3K^2/3. Does this production function have upper and...
a. A firm has the production function X =L^1/3K^2/3. Does this production function have upper and lower ridge lines? If no, explain why. If yes, derive the equations of upper and lower ridge lines.
b. Now suppose that a different production function is given as: X=12−(27−L)^1/3(8−K)^2/3 where L and K is nonnegative. Does this production function have upper and lower ridge lines? If no, explain why. If yes, derive the equations of upper and lower ridge lines.
c. Suppose that the wage rate w is $4 and the rental price r is $8. Derive the equation of expansion path of two production function given in (a) and (b) above.
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a. A firm has the production function X =L^1/3K^2/3. Does this
production function have upper and...
A firm has the production function ?= ?1/3?2/3.Does this production function have upper and lower ridge...
A firm has the production function ?= ?1/3?2/3.Does this production function have upper and lower ridge lines? If no, explain why. If yes, derive the equations of upper and lower ridge lines. Now suppose that a different production function is given as: ?= 12−(27−?)1/3(8−?)2/3 where L and K is nonnegative. Does this production function have upper and lower ridge lines? If no, explain why. If yes, derive the equations of upper and lower ridge lines. Suppose that the wage rate...
Suppose that a companies production function is given by: f(L;K) = (10K^3L^2)/(L+K) a) Does this production...
Suppose that a companies production function is given by: f(L;K) = (10K^3L^2)/(L+K) a) Does this production function exhibit increasing, constant, or decreasing returns to scale? Algebraically justify your answer. b) If there is a wage of 10 and a rental rate of capital of 1, then find the company's expansion path.
Suppose a firm’s production function is given by q = min{3K,6L}, where K is capital and...
Suppose a firm’s production function is given by q = min{3K,6L}, where K is capital and L is labor. If the wage increases, what happens to the firm’s use of labor in production (relative to capital)? Explain.
A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production...
A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production technology exhibit increasing, constant, or decreasing returns to scale? (b) Suppose that the rental rate of capital is r = 1, the wage rate is w = 1, and the ?rm wants to produce Q = 3. In the long-run, what combination of L and K should they use? (It would be good to practice doing this with the Lagrangian, even if you can...
Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function 1S:...
Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function 1S: where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 1 kg of kiwi fruits and 3 hours of labour, he can produce 1 bottle of juice a) Draw isoquants for q, q 2 and q 3 on a diagram with labour on horizontal axis and kiwi fruits on vertical b) Let the price...
4. Short questions: A firm has production function f(K, L) = 2L + 3K. The price of L is w and the...
4. Short questions: A firm has production function f(K, L) = 2L + 3K. The price of L is w and the price of K is r. Derive the cost function of the firm. a. b. A firm in a competitive industry takes account of the fact that the demand curve it faces has a negative slope. True or false? C. A profit-maximizing firm continues to operate even though makes negative profits. It sells its product at a price of...
Suppose that a rm's production function is Y = (3)L^(1/4)K ^(1/2), where L is the number...
Suppose that a rm's production function is Y = (3)L^(1/4)K ^(1/2), where L is the number of employees, K is the amount of capital, and Y is the quantity of output. The wage rate is w= 4, the rental rate of capital is r = 1, and the output price is p= 6. What are the optimal L and K in the long-run? What's the long-run profit?
Problem 3. A profit-maximizing firm produces apples, and its production function is (L)- where L is...
Problem 3. A profit-maximizing firm produces apples, and its production function is (L)- where L is the level of labor. Suppose the wage isw-1. The price of one apple is denoted by pa 1. Determine the marginal product of labor. Does the production function exhibit dimin ishing marginal product? Explain why. 2. Determine the cost function c(g) What is the implication of diminishing marginal product on the cost function? 3. Find the optimal production level (pa). Plot the (inverse) supply...
Consider a production function Q = 3K + 4L, when L is graphed on the x-axis...
Consider a production function Q = 3K + 4L, when L is graphed on the x-axis and K is graphed on the y-axis, the marginal rate of technical substitution is equal to A) 4/3 and the isoquant is convex to the origin. B) 4/3 and the isoquant is a straight line. C) and the isoquant is a straight line. D) 12 and the isoquant is convex to the origin.
Question 2: A firm producing hockey sticks has a production function given by q= 8k0.5l 0.5...
Question 2: A firm producing hockey sticks has a production function given by q= 8k0.5l 0.5 In the short run, the firm’s amount of capital equipment is fixed at k=25. The rental rate for k is v=$1 and the wage rate for l is w=$4. (a) Calculate the firm’s total cost function, average cost function and marginal cost function in the short run. (b) What are the SC, SAC and SMC for the firm if it produces 25 hockey sticks?...
Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function 1S: where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 1 kg of kiwi fruits and 3 hours of labour, he can produce 1 bottle of juice a) Draw isoquants for q, q 2 and q 3 on a diagram with labour on horizontal axis and kiwi fruits on vertical b) Let the price...
4. Short questions: A firm has production function f(K, L) = 2L + 3K. The price of L is w and the price of K is r. Derive the cost function of the firm. a. b. A firm in a competitive industry takes account of the fact that the demand curve it faces has a negative slope. True or false? C. A profit-maximizing firm continues to operate even though makes negative profits. It sells its product at a price of...
Problem 3. A profit-maximizing firm produces apples, and its production function is (L)- where L is the level of labor. Suppose the wage isw-1. The price of one apple is denoted by pa 1. Determine the marginal product of labor. Does the production function exhibit dimin ishing marginal product? Explain why. 2. Determine the cost function c(g) What is the implication of diminishing marginal product on the cost function? 3. Find the optimal production level (pa). Plot the (inverse) supply...
Consider a production function Q = 3K + 4L, when L is graphed on the x-axis and K is graphed on the y-axis, the marginal rate of technical substitution is equal to A) 4/3 and the isoquant is convex to the origin. B) 4/3 and the isoquant is a straight line. C) and the isoquant is a straight line. D) 12 and the isoquant is convex to the origin.
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