Question

14. A firm’s production function is Q = 12*L0.5*K0.5. Input prices are $36 per labor unit...

14. A firm’s production function is Q = 12*L0.5*K0.5. Input prices are $36 per labor unit and $16 per capital unit. The product’s price is P = $10. (Given: MP(L) = 6*L-0.5*K0.5; and MP(K) = 6*L0.5*K-0.5)

In the short run, the firm has a fixed amount of capital, K = 9. Calculate the firm’s profit-maximizing employment of labor. (Note: short term profit maximization condition: MPR(L) = MC(L) )

In the long run, suppose the firm could adjust both labor and capital. Calculate the least cost input proportions (i.e. K/L or L/K). (Note : In the long run the least cost input condition : MP(L)/PL = MP(K)/PK.)

Business   Economics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
3. Consider the production function, Q = [L0.5 + K0.5] 2 . The marginal products are...
3. Consider the production function, Q = [L0.5 + K0.5] 2 . The marginal products are given as follows: MPL = [L0.5 + K0.5] L-0.5 and MPK = [L0.5 + K0.5] K-0.5 and w = 2, r = 1. A). what is the value of lambda B). Does this production function exhibit increasing, decreasing or constant returns to scale? C).Determine the cost minimizing value of L D).Determine the cost minimizing value of K E).Determine the total cost function F).Determine the...
1. A firm production function is given by q(l,k) = l0.5·k0.5, where q is number of...
1. A firm production function is given by q(l,k) = l0.5·k0.5, where q is number of units of output produced, l the number of units of labor input used and k the number of units of capital input used. This firm profit function is π = p·q(l,k) – w·l – v·k, where p is the price of output, w the wage rate of labor and v the rental rate of capital. In the short-run, k = 100. This firm hires...
A firm has production function q=10*(L0.5)*(K0.5). In the short term, capital K is fixed at 9....
A firm has production function q=10*(L0.5)*(K0.5). In the short term, capital K is fixed at 9. (a) What is the multiplicative constant term in the firm's short-run inverse demand for labor? (b) What is the multiplicative constant term in the firm's short-run direct demand for labor? (c) What is the multiplicative constant term in the firm's long-run inverse demand for labor?
A firm’s production function is q = 10KL with per unit input prices for labor w...
A firm’s production function is q = 10KL with per unit input prices for labor w = 3 and capital r = 2. Support your answers with a graph of isoquant-isocosts. a. Calculate the least-cost input combination of L and K to produce 60 units of output. b. Suppose the wage decreases to $2. How does this affect input use holding constant output at 60? c. What are the total costs of producing the two output levels in parts (a)...
A firm produces good Q using inputs L & K. The firm’s production function is X...
A firm produces good Q using inputs L & K. The firm’s production function is X = 20L^0.5 + 11K. The price of K is $P_K a unit and the price of L is $P_L a unit, and in the short‐run, the capital input is fixed at 3 units. a. If the firm needs an output of X_1 in the short‐run, what is the firm’s total cost and marginal cost of production? b. What is the firm’s fixed cost and...
A competitive firm’s production function is             Q = 5 + 20L - .5L2 + 40K...
A competitive firm’s production function is             Q = 5 + 20L - .5L2 + 40K – K2, and its demand function is             PQ = MRQ = d = $6. The input prices of L and K are PL = $6 and PK = $12. Use Excel to find the profit-maximizing and cost minimizing amounts of L and K to employ.   L = _______ K = _____ Find the cost minimizing ratios of marginal product to input prices: Ratios...
A firm produces a product with labor and capital. Its production function is described by Q...
A firm produces a product with labor and capital. Its production function is described by Q = min(L, K). Let w and r be the prices of labor and capital, respectively. a) Find the equation for the firm’s long-run total cost curve as a function of quantity Q and input prices, w and r. b) Find the solution to the firm’s short-run cost minimization problem when capital is fixed at a quantity of 5 units (i.e., K = 5). Derive...
Firm B’s production function is q = min {8L, 10K} where L is the quantity of...
Firm B’s production function is q = min {8L, 10K} where L is the quantity of labor and K is the quantity of capital used to produce output q. Let PL and PK denote price of labor and price of capital, respectively. Derive Firm B’s long-run total cost function. Show your work.
A firm produces output (y), using capital (K) and labor (L). The per-unit price of capital...
A firm produces output (y), using capital (K) and labor (L). The per-unit price of capital is r, and the per-unit price of labor is w. The firm’s production function is given by, y=Af(L,K), where A > 0 is a parameter reflecting the firm’s efficiency. (a) Let p denote the price of output. In the short run, the level of capital is fixed at K. Assume that the marginal product of labor is diminishing. Using comparative statics analysis, show that...
A  firm’s production function is Q = K^0.5L^0.5. The prices of the applied inputs are pK =...
A  firm’s production function is Q = K^0.5L^0.5. The prices of the applied inputs are pK = $2, pL = $2. The firm would like to know the maximum output that can be produced for $8,000. Find the combination of inputs that maximizes output for a cost of $8,000, the amount of output that can be produced, and identify the expansion path.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT