Suppose a firm is producing 2,475 units of output by hiring 50 workers (W = $20 per hour) and 25 units of capital (R = $10 per hour). The marginal product of labor and marginal product of capital are 30 and 15, respectively. Is the firm minimizing the cost of producing 2,475 units of output? Explain.

Consider the table below that describes the production function for a good (Q) in terms of inputs labor (L) and capital (K) in the short run. K L Q 10 0 0 10 1 15 10 2 30 10 3 50 10 4 60 10 5 65 10 6 68 What is the marginal product of labor for the fourth worker? Enter the number below.

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.

Suppose that a firm has the following production function: q = 2L + K. The wage for a $10 per hour and the rental rate of capital is r = worker is w $10 per hour. In the short run the firm amount of capital is fixed at K = 20 units. If the firm's goal is to minimize their cost of producing 100 units, then in the short run they will hire units of labor and in the long run they will hire units of labor. (Round answers to two decimals if necessary.)

Suppose a short-run production function is described as Q=30L-0.05L^2 where L is the number of Labors used each hour. If each unit of output (Q) has a marginal revenue (price) of $5 and the marginal cost of labor is $40 per labor unit (L), how many units of labor (L) should be hired to maximize profit?

The production function for a product is given by q = 100KL. Its marginal product functions are MPL = 100K and MPK = 100L. If the price of capital, r, is $120 per day and the price of labor, w, is $30 per day, what is the minimum cost of producing 20,000 units of output? The minimum cost of producing 20,000 units of output is $. (Round all intermediate results to 3 decimal places and enter your response rounded to two decimal places.)

The production function is y = min{x1 , x2} where x1 and x2 are the amounts of two inputsused. The price of x1 is $18 and the price of x2 is $20.a. If the firm wants to produce y = 120 units of output, how much is the (minimum)cost? b. What is the firm’s total cost function c(y)? (

Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is: q= 4K^L+ where q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. K For this production, MP, =| L and MP, = 34 K K The weekly cost function for the paper plant is C=10K+2L where C is the total weekly cost How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper each week, and how much will hiring these inputs cost them?

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?

Find the MRTS for a firm with production function f(L,K)=(L)^2+vK. Is it diminishing?