A) perfect Complement technology
So, Q3 = Min(L,K)
Isoquants are L shaped, Kinked along K = L
Graph
B) at long run cost minimization
L = K = Q3
So TC = wL + rK
TC = (1+t)Q3 + Q3
TC = Q3(2+t)
- Julia operates a cost-minimizing firm that produces a single output using labor (L) and capital...
A firm produces output Q by using capital K and labor L in fixed proportions, i.e. Q = F (K ,L ) = min {K, L/3}. The price of a unit of labor is w = 6, the price of a unit of capital is r = 2 and the price of output is p = 20. a) Draw the isoquant for Q = 8. b) Find the marginal product of labor. Suppose that (in part c and d) the...
Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firms Production function is given by Q = 5L + 15K. The price of Capital is $20 per unit and the price of Labor is $8 per unit. a) (4 points) What is the firm’s Total Cost function? TC(Q) = ____________________________ b) (8 points) Suppose the firm is producing 30 units of output (Q = 30). Using a graph, draw the firm’s isoquant for...
2. A firm produces a product with labor and capital. Its production function is described by Q = L1/2K1/2 The price of labor is w = 1, while that of capital is r = 4. (a) What is the cost-minimizing input bundle when Q = 60? (b) What is the cost-minimizing input bundle when = 30? (c) The desired output level falls from -60 to Q = 30, what is the new long-run cost-minimizing input bundle? (d) In the short-run,...
2. (12 total points) Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firm's production function is given by Q = 5L + 15K. The price of Capital is $20 per unit and the price of Labor is $8 per unit. a) (4 points) What is the firm's Total Cost function? TC(Q)= b) (8 points) Suppose the firm is producing 30 units of output (Q = 30). Using a graph, draw the firm's...
A firm uses labor L and capital K to produce output according to . Wages are and the rental rate of capital is , regardless of output. a) The firm is cost-minimizing. Solve for K and L as functions of Q. Find the equations for total cost and average cost. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
1. There is a furniture manufacturer using labor (L) and capital (K) to produce tables. Its production function is given by q= 10L^.75 K^.40. It pays a wage of $5 per hour and rents capital at a rate of $15. The firm wants to find the cost-minimizing bundle of inputs to produce 10,000 tables. Assume K is on the y-axis in what follows. Write out the firm’s cost function. Calculate the firm’s isocost equation. What is the slope of the...
1. Suppose a firm is producing output according to Q=1001KL. A. Draw a sketch of this firm's isoquant map B. What equation do you use to find a cost-minimizing combination of inputs for a certain output level Q.? K C. The marginal products of labor and capital are given by MP, = 50, and L MPK = 50, L respectively. The price of labor is $5 per unit, and the price of K capital is $20 per unit. What is...
5. Output price and supply in the short and long run Aa Aa E Consider a firm that is originally producing along the isoquant corresponding to 800 units of output using the cost-minimizing bundle of labor and capital given by point A. The current price of output is $30. CAPITAL NsOogst1 Isocost2 LO IQ (Q=800) 19(Q=400) IQ (Q=150) LABOR Now suppose the price of output falls from $30 to $20, shifting the isocost curve from Isocost1 to Isocost2. This will...
#3 3. The isoquant map for a firm that produces output with labor and capital is shown on the next page. The price of labor is $20 per unit and the price of capital is $60 per unit. a) Draw the isocost lines for expenditures of TC =$300 and TC -$360. b) How many units of labor and how many units of capital should the firm hire to minimize the cost of producing Q. units of output? EXPLAIN. c) What...
21. 12 points Consider a firm that produces output using labor (L) and capital (K). Sup- pose the firm's production technology is f(L, K) = L+ VK and the input prices are w and r for the wage and rental rate of capital. Find the firm's profit maximizing demands for labor and capital. 2.c.K