Suppose that a firm’s production costs as a function of the level of output, x, are given by the function C(x) (this is the firm’s total cost). The firm’s average cost per-unit can then be written as total cost divided by the level of output:AC(x) =C(x)x. Using the definition of average cost and your knowledge of calculus (hint: derivatives) formally prove the following statement:A firm’s average cost is increasing only when its marginal cost is greater than its average cost.
Suppose that a firm’s production costs as a function of the level of output, x, are...
2. Suppose that a firm’s production function is Q = 10 L½ K½ and the unit cost of labor is $20, capital is $80, and the product price is $12 per unit. The firm is currently producing 100 units of output and has determined that its cost minimizing quantities of labor and capital usage for this level of output is 20 and 5 respectively. The product price is $12 per unit. a. Determine the current total cost for 100 units,...
Suppose a firm’s production function is Y=f(K,L) and has the following: Output = 5,000 Wage rate = 40 Marginal product of labor = 5 Labor = 100 Rental rate = 250 Capital = 75 Marginal Product of capital = 20 Price = 10 A. What is the firm’s total revenue? B. What is the firm’s total cost? C. What is the profit for the firm? D. What is the real wage rate for this firm? E. What is the real...
Suppose that firm’s production function is Q=min {2K, 4L}, and r=8$ and w=16$. Find the firm’s long-run total cost and average cost in terms of output.
Suppose in the short run a firm’s production function is given by Q = L1/2*K1/2, and that K is fixed at K = 49. If the price of Labor, w = $6 per unit of Labor, what is the firm’s Marginal Cost of production when the firm is producing 28 units of output?
Suppose in the short run a firm’s production function is given by Q = L1/2*K1/2, and that K is fixed at K = 36. If the price of Labor, w = $12 per unit of Labor, what is the firm’s Marginal Cost of production when the firm is producing 48 units of output? MC = ________________________
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 = ½ L-1/2K1/2and MPK = ½ L1/2K-1/2 a) Suppose the price of labor is w = 18, and the price of capital is r = 2. Derive the firm’s total cost function. b) What is the firm’s marginal cost? c) For this problem, you will sketch the graph of the firm’s isoquant for Q...
Suppose the representative firm’s production function is Y = zK 0.5N 0.5 . A. Find the marginal product of labour. Are there diminishing returns to labour? B. If the real wage paid to labour is w, determine the representative firm’s demand for labour (Nd ) as a function of w, A and K, assuming the firm maximizes profit. C. Find and interpret the following derivatives: (∂N d /∂w), (∂N d /∂z), (∂Nd /∂K). D. Draw rough graphs to explain what...
Suppose a firm produces an output level according to the simple production function: Q = 5 L K, which implies M P L = 5 K and M P K = 5 L. Further suppose a firm must pay labor (L) a wage rate (w) of $5 per unit, and the rental rate (r) on capital (K) is $25 per unit. A. Find the marginal rate of technical substitution. B. Write the equation for the isocost line. What is the...
Suppose the firm's production function is Q = 2KL where Q is units of output, K is units of capital (which are fixed at 2), and L is units of labor. a. What is the firm’s short-run production function? b. Over the labor input usage range of 0 to 5, that is L ranging from 0 to 5, graph the firm’s Total Product curve. c. Derive and graph the firm’s Average Product curve and the Marginal Product curve. Graph/plot them...
_____ cost is the cost per unit at the level of production; it equals total costs divided by production a. target b. average c. marginal d. opportunity e. fixed