Question

In: Economics

Suppose your production function for baseball bats is f(K, L) = L^1/5 K^1/5 and you are...

Suppose your production function for baseball bats is f(K, L) = L^1/5 K^1/5 and you are a profit maximizing price taker. Use minimizing costs to:

(a) Determine the conditional factor demands for labor and capital (L = g(w, r, y) =? and K = h(w, r, y) =?). Use these to derive the cost function.

(b) Derive the marginal and average cost functions.

(c) Derive the supply function for baseball bats.

(d) Given this supply function, use the conditional factor demands in part a) to determine the actual factor demands (L* = L*(w, r) =? and K = K*(w, r) =?)

Expert Solution

The production function is given to be . The cost of production would be .

(a) The condition for cost minimization would be that or or or or . Now, putting it in the production function, we have or or or , and since , we have or . These are the required labor and capital that would minimize cost and maximize profit, for the given values.

The cost function would be or or or .

(b) The marginal cost would be or . The average cost would be or .

(c) The supply function would be where the price is equal to the marginal cost, ie or or .

(d) Putting in the factor demands, we have or or , and or or . For the given P and Y, these are the actual factor demands.

Rahul Sunny answered 1 year ago

Suppose a production function is given by F ( K , L ) = K 1 2...

Suppose a production function is given by F ( K , L ) = K 1 2 L 1 2, the price of capital “r” is $16, and the price of labor “w” is $16. a. (5) What combination of labor and capital minimizes the cost of producing 100 units of output in the long run? b. (5) When r falls to $1, what is the minimum cost of producing 100 pounds of pretzels in the short run? In the long...

2. Suppose a production function is given by F ( K , L ) = K 1...

2. Suppose a production function is given by F ( K , L ) = K 1 2 L 1 2, the price of capital “r” is $16, and the price of labor “w” is $16. a. (5) What combination of labor and capital minimizes the cost of producing 100 units of output in the long run? b. (5) When r falls to $1, what is the minimum cost of producing 100 pounds of pretzels in the short run? In the...

Suppose a production function is given by F ( K , L ) = K^(1/2) L^(1/2), the...

Suppose a production function is given by F ( K , L ) = K^(1/2) L^(1/2), the price of capital “r” is $16, and the price of labor “w” is $16. a. (5) What combination of labor and capital minimizes the cost of producing 100 units of output in the long run? b. (5) When r falls to $1, what is the minimum cost of producing 100 pounds of pretzels in the short run? In the long run? c. (5) When...

1. Suppose that the production function for Sevillia can be represented as Y=F (K, L) =5...

1. Suppose that the production function for Sevillia can be represented as Y=F (K, L) =5 K2/3L1/3 Assume the rate of growth of population is 20%, the saving rate is s = 0.2 and that depreciation rate is 10%. Determine the production function per worker. ( 2 marks) Calculate the steady-state capital stock per worker, output per work er, and consumption per worker. ( calculate to 2 decimal places) ( 3 marks) Illustrate the impact of implementing the policy of...

Suppose that output Q is produced with the production function Q = f(K;L), where K is...

Suppose that output Q is produced with the production function Q = f(K;L), where K is the number of machines used, and L the number of workers used. Assuming that the price of output p and the wage w and rental rate of capital r are all constant, what would the prot maximizing rules be for the hiring of L and K? (b) What is theMRTSK;L for the following production function: Q = 10K4L2? Is this technology CRS, IRS or...

Suppose that output Q is produced with the production function Q = f(K,L), where K is...

Suppose that output Q is produced with the production function Q = f(K,L), where K is the number of machines used, and L the number of workers used. Assuming that the price of output p and the wage w and rental rate of capital r are all constant, what would the proﬁt maximizing rules be for the hiring of L and K? (b) What is the MRTSK,L for the following production function: Q = 10K4L2? Is this technology CRS, IRS...

Suppose that the production function for your firm is given by: F(L,K)=L1/2K1/2 w=$1 and r=$1. In...

Suppose that the production function for your firm is given by: F(L,K)=L1/2K1/2 w=$1 and r=$1. In the long-run, how many workers and capital should you hire in order to produce Q units of output? Select one: a. L=2Q; K=Q b. L=Q; K=Q2 c. L=0.5Q; K=0.5Q d. L=Q; K=Q e. None of the above

Consider the production function F(L,K) = L^2/3 K^2/3 . (f) Does this production function exhibit increasing,...

Consider the production function F(L,K) = L^2/3 K^2/3 . (f) Does this production function exhibit increasing, decreasing or constant returns to scale? Explain. (g) Find the total cost, average cost and marginal cost of producing y units of output. Is the average cost increasing or decreasing in y? Is the marginal cost higher or lower than the average cost? Question 2 The production of magic chairs requires only two inputs: seats (S) and legs (L) (no other inputs are required...

1. • Country A and country B both have the production function Y 5 F(K, L)...

1. • Country A and country B both have the production function Y 5 F(K, L) 5 K1/3L2/3. a. Does this production function have constant returns to scale? Explain. b. What is the per-worker production function, y 5 f (k)? c. Assume that neither country experiences population growth or technological progress and that 20 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 30 percent of output...

Suppose a production function is given by f(K,L) = KL1/3 and that the price of capital...

Suppose a production function is given by f(K,L) = KL1/3 and that the price of capital is $10 and the price of labor is $16. The capital is fixed at the level K ̅ = 4. What is the quantity of labor that minimizes the cost of producing any given output? What is the minimum cost of producing y units of output? What are the marginal cost of production and the average total cost, average variable cost and the average...