A rm has production function q = K^1/3 L^2/3. Input prices are w = 1 for...

A rm has production function q = K^1/3 L^2/3. Input prices are w = 1 for labor (L), and r=1 for capital (K).

a. Write down the firm's Cost Minimization Problem. Derive the optimality conditions.

b. Define the optimal choice of inputs, i.e. solve the Cost Minimization problem above for K and L.

c. What is the total cost to produce q=4 units of output?

Expert Solution

Rahul Sunny answered 1 year ago

2. Consider a firm with the following production function: Q = K 1/3 L 2/3 (a)...

2. Consider a firm with the following production function: Q = K 1/3 L 2/3 (a) Consider an output level of Q = 100. Find the expression of the isoquant for this output level. (b) Find the marginal product of labor, MPL. Is it increasing, decreasing, or constant in the units of labor, L, that the firm uses? (c) Find the marginal product of capital, MPK. Is it increasing, decreasing, or constant in the units of capital, K, that the...

A plant’s production function is Q = L^1/3 K^2/3, where L is hours of labor and...

A plant’s production function is Q = L^1/3 K^2/3, where L is hours of labor and K is hours of capital. The price of labor services, w, is $40 per hour and of capital services, r, is $10 per hour. a. Derive the long-run expansion path. In words describe what the expansion path represents. b. In the short-run, the plant’s capital is fixed at K = 64. Labor, on the other hand, is variable. How much will it cost to...

Consider production function Q= L^3 * K^4 - L^2 (a) Determine the MRTS L,K for this...

Consider production function Q= L^3 * K^4 - L^2 (a) Determine the MRTS L,K for this production function (b) Does this production function have an uneconomic region? If so, describe the region algebraically. (Hint: your answer will be an inequality like this: K<5L)

Suppose that the firm has a production function described by q=0 if L≤6 q = −(L^3)/6+K(L^2)+26K...

Suppose that the firm has a production function described by q=0 if L≤6 q = −(L^3)/6+K(L^2)+26K if L>6 Further suppose that we are concerned only in the short run and that the units of capital employed are currently fixed at 8. Also, suppose that labor units are integer. That is, they can only be in terms of whole numbers 1, 2, 3, ... and so on. Suppose that the price of each unit produced by the firm is 2. 1....

1. Answer the following using the production function F(L, K) = L1/2K1/2, input prices fixed at...

1. Answer the following using the production function F(L, K) = L1/2K1/2, input prices fixed at w =4 and v = 9. There are two different types of firms. Big firms have SR capital fixed at 144, and small firms have SR fixed capital of 64. a) Show that for the big firms with K = 144, SCb(q) = q2 /36 + 1296 and for the small firms with fixed capital of 64, SCs(q) = q2/16 + 576. Use this...

A firm has production function q = 100 L + KL− L^2 − K^2 The price...

A firm has production function q = 100 L + KL− L^2 − K^2 The price of the good is $1. The wage is $10, and the price of capital is $30. Assume that the firm is a price - taker in a perfectly competitive market. a. What will the firm’s profit maximizing choice of capital and labor be? b. Suppose that the firm’s capital is fixed in the short-run and wage rises to $20. What is the firm’s new...

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...

Suppose the production function of a firm is given by q=L^1/4 K^1/4. The prices of labor...

Suppose the production function of a firm is given by q=L^1/4 K^1/4. The prices of labor and capital are given by and w=10 and r=20, respectively. Write down the firm’s cost minimization problem. What returns to scale does the production function exhibit? Explain. What is the Marginal Rate of Technical Substitution (MRTS) between capital and labor? What is the optimal capital to labor ratio? Show your work.

The production function has two input, labor (L) and capital (K). The price for L and...

The production function has two input, labor (L) and capital (K). The price for L and K are respectively W and V. q = L + K a linear production function q = min{aK, bL} which is a Leontief production function 1.Calculate the marginal rate of substitution. 2.Calculate the elasticity of the marginal rate of substitution. 3.Drive the long run cost function that is a function of input prices and quantity produced.

2. A firm’s production function is given by q= L^1/2+ K. The price of labour is...

2. A firm’s production function is given by q= L^1/2+ K. The price of labour is fixed at w = 1, and the price of capital is fixed at r = 8. a. Find the firm’s marginal rate of technical substitution. b. Suppose both labour and capital can be varied by the firm, and that the firm wishes to produce q units of output. Use the answer to (a) to find the cost-minimising amounts of labour and capital (as functions...

Question