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Profit is maximised when first derivative is zero and second derivative is negative
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A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the...
Consider a production function Q=Q(K,L)=6K^(1/2)L^(1/3) with K as capital and L as labor input. Let the...
Consider a production function Q=Q(K,L)=6K^(1/2)L^(1/3) with K as capital and L as labor input. Let the price per unit of output be P=$0.50, the cost or rental rate per unit of capital be r=$0.10 and let the price (wage rate) of labor be w=$1. a) find the profit max level of K and L and check with second order condition (my answer was L=3.375 and K=1.5) b) Find max profit (I got profit=1.986)
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...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the units of output and L is the number of labor hours. Each output sells for 100 dollars per unit. The human resources manager estimates that the marginal cost of hiring an extra worker is 50 dollars. How many labor hours should this firm hire? Hint: MPL=5-2 L 1) 2) A frim's production function is given by Q(L)-6L, where Q measures output and L is...
A firm produces output according to the production function: Q = F(K,L) = 2K + 2L....
A firm produces output according to the production function: Q = F(K,L) = 2K + 2L. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $65 per hour and the rental rate on capital is $35 per hour, what is the cost-minimizing input mix for producing 4 units of output? Capital: Labor:
Suppose the firm's production function is given by q= F(K, L)= K2L with MPL=K2, MPK=2KL The...
Suppose the firm's production function is given by q= F(K, L)= K2L with MPL=K2, MPK=2KL The price per unit of capital is 10 and the price per unit of labor is 5. Find the cost minimizing quantity of labor to produce 500,000 units of output. Please round to the closest integer.
2. Suppose that a firm’s production function is Q = 10 L½ K½ and the unit...
2. Suppose that a firm’s production function is Q = 10 L½ K½ and the unit cost of labor is $20, capital is $80, and the product price is $12 per unit. The firm is currently producing 100 units of output and has determined that its cost minimizing quantities of labor and capital usage for this level of output is 20 and 5 respectively. The product price is $12 per unit. a. Determine the current total cost for 100 units,...
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...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital,...
10. Consider the production function: f(KL)=K L. Let wandr 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 as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
3. Suppose that the firm's production function is Q = min{2L, K}. Suppose hourl wage is $10 and hourly rent for cap...
3. Suppose that the firm's production function is Q = min{2L, K}. Suppose hourl wage is $10 and hourly rent for capital is $20. What is the long-run total cost curve?
Suppose the production function is given by Q = K 1/2L 1/2, and that Q =...
Suppose the production function is given by Q = K 1/2L 1/2, and that Q = 30 and K = 25. How much labor is employed by the firm? Answers: 49. 6. 36. 25.
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...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the units of output and L is the number of labor hours. Each output sells for 100 dollars per unit. The human resources manager estimates that the marginal cost of hiring an extra worker is 50 dollars. How many labor hours should this firm hire? Hint: MPL=5-2 L 1) 2) A frim's production function is given by Q(L)-6L, where Q measures output and L is...
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...
10. Consider the production function: f(KL)=K L. Let wandr 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 as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
3. Suppose that the firm's production function is Q = min{2L, K}. Suppose hourl wage is $10 and hourly rent for capital is $20. What is the long-run total cost curve?
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