Question

Suppose you own a firm that producing shoes using both capital and labor. The production function...

Suppose you own a firm that producing shoes using both capital and labor. The production function is q=f(K, L)=0.5K2 L4 . In long run both capital (K) and labor (L) are variable. Price for each pair of shoes is $50 (p=50), the wage rate is 0.04 (w=0.04) and the rental price for capital is 1 (r=1). Given those output and input prices, what is the profit maximizing input level of K and L (K* & L* )?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider a firm using the production technology given by q = f(K, L) = ln(L^K) If...
Consider a firm using the production technology given by q = f(K, L) = ln(L^K) If capital is fixed at K = 2 units in the short run, then what is the profit maximizing allocation of output if the price of output and respective input prices of labor and capital are given by (p, w, r) = (2, 1, 5)?
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...
2. Suppose a firm is producing 200 widgets. The firm’s production function is Cobb- Douglas with...
2. Suppose a firm is producing 200 widgets. The firm’s production function is Cobb- Douglas with decreasing returns to scale. (This means we have normal, convex isoquants). The firm uses K’ units of capital and L’ units of labor. Initially, the input prices are w’ and r’. However, an exogenous shock in the labor market causes an increase in the wage rate, resulting in an increase in input prices from w’ to w’’ where w’<w’’. Using a graph (of isoquant...
A firm uses capital and labor to produce output according to the production ? = 4√??...
A firm uses capital and labor to produce output according to the production ? = 4√?? (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r=$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
a firm produces a product with labor and capital as inputs. The production function is described...
a firm produces a product with labor and capital as inputs. The production function is described by Q=LK. the marginal products associated with this production function are MPL=K and MPK=L. let w=1 and r=1 be the prices of labor and capital, respectively a) find the equation for the firms long-run total cost curve curve as a function of quantity Q b) solve the firms short-run cost-minimization problem when capital is fixed at a quantity of 5 units (ie.,K=5). derive the...
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...
FACTOR PRICES QUESTION Imagine firm Oracle is producing computers following production function q(L,K) =L^0.5 K^2. In...
FACTOR PRICES QUESTION Imagine firm Oracle is producing computers following production function q(L,K) =L^0.5 K^2. In the short run, capital is fixed at K¯ = 5. Oracle faces price p = 50 and can hire as many workers as it would like at a constant wage w = 25. A. Find equilibrium labor (L∗) and wages. B. What are Oracle’s profits at this equilibrium? C. Prove that this profit level is a global maximum.
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)...
Given production function: Q=L3/5K1/5. Where L is labor, K is capital, w is wage rate, and...
Given production function: Q=L3/5K1/5. Where L is labor, K is capital, w is wage rate, and r is rental rate. What kinds of returns to scale does your firm face? Find cost minimizing level of L and K, and long run cost function.
The Pear Corp produces high end consumer electronics using labor L and capital K according to...
The Pear Corp produces high end consumer electronics using labor L and capital K according to production function Q = F (L,K) = (100)(L^1/4)(K^1/4). Let the price of a unit of labor be given by W and the price of a unit of capital is given by R. The output price is P = 1 which Pear Corp takes as given for any choice of output level Q. Both labor and capital are fully adjustable. Set input price W =...