1. Consider a firm with the following production function: Q = KL1/2 (a) Consider an output...

1. Consider a firm with the following production function: Q = KL^1/2

(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 firm uses?

(d) Use your result in parts (b)-(c) to find the marginal rate of technical substitution, MRTS, for this firm.

(e) Is the MRTS increasing or decreasing in the units of labor, L? What does that imply about the shape of the isoquant?

(f) Given your result in part (d), what can you say about the firm’s ability to substitute one input for another? (g) Assume now that the firm were to increase all inputs by a common factor > 0. What happens to the output that the firm produces? [Hint: check whether the firm’s production function exhibits increasing, decreasing, or constant returns to scale.]

Solutions

Expert Solution

Rahul Sunny answered 3 weeks ago

Next > < Previous

Related Solutions

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...

Consider a firm with the following production function: Q = K1/2L1/2 Assume that we are in...

Consider a firm with the following production function: Q = K1/2L1/2 Assume that we are in the short run so the capital stock is fixed at 4 units. The wage rate is $16 and the rental rate of capital is $10. Please graph the firm's short run margical cost, average variable cost, average fixed cost, and average total cost curves. Remember to label the axes and curves accurately.

1. A firm operates with the production function Q=K2L. Q represents the daily output when the...

1. A firm operates with the production function Q=K2L. Q represents the daily output when the firm rents K units of capital and employs L workers. The manager has been given a production target: Produce 8,000 units per day. She knows the daily rental price of capital is $400 per unit. The wage rate paid to each worker is $200 per day. a. Currently the firm employs 80 workers per day. What is the firm’s total daily cost of producing...

A firm has a production function Q = KL, where Q is the quantity of output,...

A firm has a production function Q = KL, where Q is the quantity of output, K is the amount of capital and L is the amount of labor. MPL=K and MPK=L . a) Suppose that capital is fixed at K=10 in short run. In this case, the marginal product of labor is MPL=10. Does this production function exhibit diminishing marginal returns to labor? b) Suppose that in the short run, K is fixed at 10. The interest rate is...

A firm has the following production function: q=KL The firm will produce 64 units of output...

A firm has the following production function: q=KL The firm will produce 64 units of output and faces prices for labor and capital of $4 and $1 respectively. What is the optimal quantity of labor and capital the firm should employ in order to minimize the cost of producing 64 units of output? What is the minimum cost of producing 64 units of output? Show the firms optimal production decision on a graph.

1. Consider production function of the form Q= f(H, K), where Q is the output measure...

1. Consider production function of the form Q= f(H, K), where Q is the output measure and H and K are hours worked and gross capital stock, respectively. Based on 33 observations we obtain the following results: ?og(?) = 0.129 + 0.448 ?og (?) + 0.559 ?og (?) (Standard Error) (0.546) (0.704) (0.816) R2= 0.886 a. Interpret the regression results. b. What is the output elasticity of hours worked? c. Verify that the coefficients of log(H) and log(K) are statistically...

A firm produces output according to the following function: q = f (L, K) = L^1/2...

A firm produces output according to the following function: q = f (L, K) = L^1/2 K^1/4 . The cost of labor is $8 per hour and the rental cost of capital is $2 per hour. a. Determine the returns to scale for this function. b. Suppose the firm wishes to produce at cost $96. How much capital and how much labor does the firm employ? c. Derive the short-run cost function with optimal amount of K from part b....

Consider the firm with production function given by q = f ( L , K )...

Consider the firm with production function given by q = f ( L , K ) = L ^(1/4) K^(1/4). If w = r = 4, what is the change in the producer surplus when the price increases from $16 to $32? (round your answer to one decimal place if necessary)

Exercise 3. Consider a firm with the Cobb-Douglas production function Q = 4L^1/3*K^1/2. Assume that the...

Exercise 3. Consider a firm with the Cobb-Douglas production function Q = 4L^1/3*K^1/2. Assume that the firm faces input prices of w = $7 per unit of labor, and r = $10 per unit of capital. a) Solve the firm’s cost minimization problem, to obtain the combination of inputs (labor and capital) that minimizes the firm’s cost of production a given amount of output, Q. b) Use your results form part (a) to find the firm’s cost function. This is...

Short Run Cost Curves: Consider a firm with the following production function: q=(KL)/20 a. For a...

Short Run Cost Curves: Consider a firm with the following production function: q=(KL)/20 a. For a short-run situation in which K=10, wage = 4 and cost of capital = 1, derive expressions for short run total cost and short run average cost for this production function. b. Plot the short-run total cost curve and label it “TC1”. Now suppose that the cost of capital goes up to 2. (Continue to assume we’re in the short run and K can not...

Subjects