Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?

12. A firm’s production is represented by the following function: Q = L0.4 K0.6 . The rental rate of capital (r) is $30 and the wage rate (w) is $5. For a given level of output, what should be the ratio of capital to labor in order to minimize costs? How much capital and labor should be used to produce 600 units of output? What is the total cost? What is the short run total cost if output is decreased to 300 units? What would be the optimal choice of capital and labor in the long run in order to produce 300 units of output? What is the long-run total cost? Does this production function exhibit increasing, decreasing, or constant returns to scale? Please answer based on the cost calculations in parts c and d.

The Mini-Case "Economies of Scale at Google" describes economies of scale for Google Cloud Storage. The cost function for this service is well approximated by C = F + cq, where C is total cost, F is fixed cost, c is a constant, and q is output. What is marginal cost for this cost function? What are the average fixed costs, average variable cost, and average cost? Over what range of output does google have economies of scale?   If the general nature of this problem is bothering you let c = 10 and answer each question, then generalize to c being a constant.   Marginal cost is a contant, MC = c.

You are given the following cost functions: TC =100 + 60Q- 3Q2 + 0.1Q3 TC =100 + 60Q+ 3Q2 TC = 100 + 60Q Compute the average variable cost, average cost, and marginal cost for each function.

A firm has the following production function: q = 8KL, where q is the weekly output, K is the number of machines and L is the number of workers. Each machine rents for $50,000 per week and each worker costs $2,000 per week. The total cost includes the cost of machines and labor, as well as an additional $5,000 per unit of output for raw materials. The firm currently runs a single factory with 10 machines. Assume that capital is fixed in the short run. (a) How many workers are needed to produce 2,000 units of output per week (in the short run)? (b) How much does it cost to produce q units of output per week (in the short-run)? [The answer I expect is a particular function of q.

An economist estimated that the cost function of a single-product firm is:C(Q) = 90 + 30Q + 25Q2 + 10Q3.Based on this information, determine the following: A.The average fixed cost of producing 10 units of output.

Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost. a) Find the marginal product of each input. b) Determine whether the production function exhibits diminishing marginal product to each input. c) Find the marginal rate of technical substitution (MRTSLK) d) How does MRTSLK change as more L, is used holding output constant. e) Find the least costly combination of labour and capital to produce 3000 units.

Suppose that the production function for Hannah and Sam's home remodeling business is            Q = F(L,K)            Q = 10L0.1K0.4.Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $1,000 per week.a. What is the least-cost input combination for remodeling 400 square feet each week?      Instructions: Round your answers to 2 decimal places.      units of labor and  units of capital.  b. What is the total cost?         Instructions: Round your answer to 2 decimal places.    $  .revised jrl 08-11-2011

14. The research department of Acme, Inc. has determined the marginal cost function for one particular item to be m(x) = 0.12e0.04x dollars per item, where x is the number of items produced. If Acme's fixed costs amount to $3,000, find the cost function, C(x), for the company.

Suppose a firm’s cost function is given by: C= 50 + 4q2 a) Find the equations for AFC, AVC and MC. b) If w=$4, what’s the short run production function for this firm?