Saxxon Fifth Avenue's production function is given by Q = L+ K. Let w = 1 and r = 2 be the prices of labor and capital, respectively. (a) Find the equation of Saxxon Fifth Avenue's longrun total cost curve. Hint: Note that labor and eapital are perfect substitutes. (b) Suppose capital is fized at 5 units (i.e., K = 5) in the short run. Derive the equation for Sazzon Fifth Avenue's shortrun total cost curve. For simplicity, assume the fxed cost is sunk. (c) In a graph, draw Saxon Fifth Avenue's short-run total cost curve and longrun total cost curve.

a) Given the production function y = (l'+K®)®, what is the technical rate of substitution the elasticity of substitution, and the returns to scale when p = 0.5?

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.

5. Selpats produces pens with the production function f(k, l) = 200vkl. The price of capital is wk = 40 and the price of labor is wL = 10. (i) Determine the optimal input bundle for producing y pens in the long run and find the long-run cost function. (ii) Determine the optimal input bundle for producing y = 10,000 pens in the long run. (iii) Now suppose that capital is fixed at k = 25 in the short run. Find the short-run total cost function and the short-run marginal cost function. Explain the relationship between the short-run and long-run marginal costs when y = 10,000. (iv) Suppose that the price of output is p. Which value of y maximizes short-run profit? р.

Suppose that the production function for Hannah and Sam's home remodeling business is Q=f(L,K) Q=1040.2K0.3 Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week. a. What is the least-cost input combination for remodeling 100 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.

Consider the production function f (x1, x2)=min{x1, x2}. Assume the price of the inputs are w1 and w2. Assuming that to increase the quantity of input 1 by one unitwhile holding constant the quantity of input 2 1) show that the technology has constant returns to scale. 2) Write the cost minimization problem of thev firm

2. A firm uses capital (denoted by K) and labor (denoted by L) to produce hockey sticks. The firm's production function is given by q = 2/KL . In the short run, the firm's amount of capital equipment is fixed at K = 100. The rental rate for capital is $1 per unit and the wage rate is equal %3D to $4. a) Calculate the firm's short-run total cost function. Also, calculate the short-run average cost function. b) Calculate the firm's short-run marginal cost function. c) Graph the firm's short-run marginal and average (total, fixed, and variable) cost curves. d) Where does the short-run marginal cost intersect the short-run total average cost? Explain why this is so.

1) 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, Kis the quantity of capital rented, and L is the quantity of labor hired. For this production, MP, = and MP, = The weekly cost function for the paper plant is C= 10K +2L where C is the total weekly cost What ratio of capital to labor minimizes Miguel and Jake's total costs? (Hint: Find the Marginal Rate of Technical Substitution (MRTS) for capital and labor.) b. 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? How much will hiring these inputs cost them?

A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3?unit(s)b. If the wage rate is $45 per hour and the rental rate on capital is $25 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital:  Labor:  c. How does your answer to part b change if the wage rate decreases to $25 per hour but the rental rate on capital remains at $25 per hour? Capital decreases and labor increases. Capital and labor increase. It does not change. Capital increases and labor decreases.       Only typed answer

A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3?unit(s)b. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on capital remains at $10 per hour?multiple choice Capital and labor increase. Capital decreases and labor increases. Capital increases and labor decreases. It does not change.