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 = K^1/2L^1/2

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.

Solutions

Expert Solution

Rahul Sunny answered 2 years ago

Next > < Previous

Related Solutions

Let the production function be Q=L1/2 K1/2. Assume Capital, K=1 and the firm pays workers W...

Let the production function be Q=L1/2 K1/2. Assume Capital, K=1 and the firm pays workers W . a. Find the marginal product of labor. b. Show the production function exhibits diminishing marginal productivity. c. Show the relationship between marginal product and marginal cost d. Show marginal cost increases as output increases/

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 = KL1/2 (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)...

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 an economy with the following Cobb-Douglas production function: Y = K1/3L 2/3 .

Consider an economy with the following Cobb-Douglas production function: Y = K1/3L 2/3 . The economy has 1,000 units of capital and a labor force of 1,000 workers. 1a. Derive an equation describing labor demand as a function of the real wage and the capital stock. (Hint: this is a review from what we did in Chapter 3)b. If the real wage can adjust to equilibrate labor supply and labor demand, what is the resulting equilibrium real wage? In this...

Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor...

Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL= K1/2 / 2L1/2 & MPK = L1/2 / 2K 1/2 a) If the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output Q...

Isoquant Analysis. A firm with production function q = K1/4L1/4 operates with variable labour and variable...

Isoquant Analysis. A firm with production function q = K1/4L1/4 operates with variable labour and variable capital. The firm sells output at a competitive price p = 80 and hires labour at w = 2 and capital at r = 0.5. This firm will produce q = will hire L = will lease capital K = will incur total cost C = will earn profits π = Now the price rises to p = 120. This firm will produce q...

2. The production function is given as Q=LK1/2 with K fixed at 4 units. Note K1/2...

2. The production function is given as Q=LK1/2 with K fixed at 4 units. Note K1/2 is same as the square root of K. a. Draw the total, average and marginal product associated with this function. b. Write down the equations for total cost, total fixed and total variable cost when w=2 and r=3, and draw the respective diagrams. c. Write down the equations for AFC, AVC, MC and ATC corresponding to the values of w and r as in...

Consider the following production function q = K a L b. Assume that a+b>1. Assume that...

Consider the following production function q = K a L b. Assume that a+b>1. Assume that the firm takes price of labor w, price of capital r and price of the final product p as given and minimizes costs to produce a given level of output q. Find the share of labor cost in total value of the product wL/pq as a function of q, input prices, a and b (there should not be p in your function). How does...

Consider an economy with the following production function: Y = K1/2N1/2. The economy has 1,000 units...

Consider an economy with the following production function: Y = K1/2N1/2. The economy has 1,000 units of capital and 1,000 workers. a) Derive the labor demand curve for this economy, (Recall that the real wage, w = MPN. This can be used to solve for N as a function of the other variables). b) If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage rate? c) Suppose that Congress, concerned about the...

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...

Subjects