Suppose producer’s production function let q(K, E) = K0.5E0.5 Suppose producer’s cost function if w=w’ and...
Suppose producer’s production function let q(K, E) = K0.5E0.5
Suppose producer’s cost function if w=w’ and r = r’
Suppose w = 10 and r = 15
Suppose you must make 1500 units of q spending least money possible (min cost)
Rewrite this as a single variable optimization problem
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Suppose producer’s production function let q(K, E) =
K0.5E0.5
Suppose producer’s cost function if w=w’ and...
7. Suppose a firm's production function is Q-min(L,K). (This means the level of O produced is...
7. Suppose a firm's production function is Q-min(L,K). (This means the level of O produced is the smaller of L and K) a. Graph some isoquants for this firm. b. Let w = 2, r= 1, and suppose the firm's expenditures are C-12. What are the firm's demands for L and K? What is the share of labor in the cost of output? c. Now let w rise to 3. What are the firm's new demands for L and K?...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm e...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
4. Suppose the production function is equal to the following: Q = (√L)(K) Suppose the price...
4. Suppose the production function is equal to the following: Q = (√L)(K) Suppose the price of capital is equal to r, the price of labor is equal to w, and capital is fixed at 10 units. a) Determine the Cost function. b) Determine the marginal cost of producing an additional unit of output. c) Determine the average variable cost.
7. For the production function q= min(K, 4L) (a) Assume that capital K is fixed at...
7. For the production function q= min(K, 4L) (a) Assume that capital K is fixed at 100 units. Derive and plot Page 2 of . The total product function q(L) ii. The marginal product function MPL(L) ii. The average product function AP(L) (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short...
7. For the production function q min(K,4L ): (a) Assume that capital K is fixed at...
7. For the production function q min(K,4L ): (a) Assume that capital K is fixed at 100 units. Derive and plot: i, The total product function q(L) ii. The marginal product function MPL(L). iii. The average product function APL(L). (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short run average cost....
Suppose that a firm had a production function given by q-21 K The rental rate for...
Suppose that a firm had a production function given by q-21 K The rental rate for the fim is $10 and the wage is s5 Solve the optimization condition for K and then fill in the value that appears in front of L K- Round to the nearest 2 decimal places if necessary.) Suppose that a firm had a production function given by q-L025k075. The wage rate (w) is $10 and the rental rate () is $10 Calculate the amount...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function. 12. Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
Suppose that a firm had a production function given by: q=L^0.25*K^0.75. The wage rate (w) is...
Suppose that a firm had a production function given by: q=L^0.25*K^0.75. The wage rate (w) is $10 and the rental rate (r) is $20. Calculate the amount of labor the firm would hire when it produces 300 units of output in a cost-minimizing way
7. Suppose a firm's production function is Q-min(L,K). (This means the level of O produced is the smaller of L and K) a. Graph some isoquants for this firm. b. Let w = 2, r= 1, and suppose the firm's expenditures are C-12. What are the firm's demands for L and K? What is the share of labor in the cost of output? c. Now let w rise to 3. What are the firm's new demands for L and K?...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
7. For the production function q= min(K, 4L) (a) Assume that capital K is fixed at 100 units. Derive and plot Page 2 of . The total product function q(L) ii. The marginal product function MPL(L) ii. The average product function AP(L) (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short...
7. For the production function q min(K,4L ): (a) Assume that capital K is fixed at 100 units. Derive and plot: i, The total product function q(L) ii. The marginal product function MPL(L). iii. The average product function APL(L). (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short run average cost....
Suppose that a firm had a production function given by q-21 K The rental rate for the fim is $10 and the wage is s5 Solve the optimization condition for K and then fill in the value that appears in front of L K- Round to the nearest 2 decimal places if necessary.) Suppose that a firm had a production function given by q-L025k075. The wage rate (w) is $10 and the rental rate () is $10 Calculate the amount...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function. 12. Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
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