A company has a production function Q = (K)0.5 + L. For this production function MPL = 1 and MPK = 0.5(K)-0.5. The firm faces w=$50 and r= $1. Keeping r =1, the price of labor, w, must fall to less than $ in order for the firm to use a positive %3D amount of capital to produce 10 units, or the output Q must increase to over units for the firm to use a positive amount of capital, at w=$50.

X and X2 are the two factors used in production A firm's production function: fcx₁, x₂) = max {x₁, X₂} the price of X, is W₁=8, and the price of X₂ is W₂=10 The firm paproduce 100 total units of output, what is the total cost?

A firm produces output according to a production function: Q = F(K,L) = min {4K,4L). a. How much output is produced when K= 2 and L = 1? unit(s) b. If the wage rate is $60 per hour and the rental rate on capital is $40 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $40 per hour but the rental rate on capital remains at $40 per hour? O Capital decreases and labor increases. O It does not change. O Capital increases and labor decreases. O Capital and labor increase.

A firm has the following production function: q = KL, where q is output, K is capital and L is labor. The price of a unit of capital is $1,000 and the price of a unit of labor is $500. The total cost includes the cost of capital and labor, as well as an additional $200 per unit of output for raw materials. The firm currently runs a single factory with 5 units of capital. Assume that capital is fixed in the short run. (a) How much does it cost to produce q units of output (in the short-run)? [The answer I expect is a particular function of q.] (b) Will the firm produce or shut down in the short run if the price of a unit of output is $300? Explain in at most one sentence.

A firm has the production function Q(L, K) = √K + 2√L. The price of one unit of capital is R> 0, and the price of one unit of labor is W> 0. Which of the following statements is correct? The production function can be represented by a CES production function [aL + bKº] for suitable values of a, b and p. The production function has increasing returns to scale. The marginal rate of technical substitution is MRTS (L, K) = 2√L VR OfW= R. the fi rm's demand for labor is four times the demand for capital.