2. Assume that a firm has the following production function; q = L0.5K0.5. Its capital is fixed at K = 1. It faces a rental rate of r = $90 and a wage rate of W = $10. d. Determine the average, average variable, and average fixed cost functions. e. Determine the marginal cost function. f. Calculate the lowest cost, and associated quantity, that the firm can produce this good for in the short run. J

2. Assume that a firm has the following production function; q = L0.5K0.5. Its capital is fixed at K = 1. It faces a rental rate of r = $90 and a wage rate of W = $10. d. Determine the average, average variable, and average fixed cost functions. e. Determine the marginal cost function. f. Calculate the lowest cost, and associated quantity, that the firm can produce this good for in the short run. J

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A production function for a good Q uses inputs of labor (L) and capital (K) and takes the form Q=LK. The wage is equal to $20 and the rental rate of capital is equal to $80. The firm has to produce a target qo. What is the equation for the firm's long-run total cost curve?
Month (m): 4 Day (d): 1 Use the two numbers above, m and d, to complete the cost function for a perfectly competitive firm: Cost (q) = m q2 + d = (30) For a cost function like yours, Marginal Cost (MC) = 2 m q . Specifically, what are the following for the cost function you wrote out above? Fixed Cost = Average Total Cost = Cost (q)/q = Variable Cost = Average Fixed Cost = FC/q = Marginal Cost = 2 m q = Average Variable Cost = VC/q = (15) Fill in the table with your values from your cost function. q Total Cost AVC AFC ATC MC 0 0 0 -- -- -- 1 2 3 4 5 6
2. Assume that a firm has the following production function; q = L0.5K0.5. Its capital is fixed at K = 1. It faces a rental rate of r = $90 and a wage rate of W = $10. a. Calculate the firm's fixed costs. b. Determine the firm's variable cost function. c. Determine the firm's short run cost curve.
COURSE: ECONOMY A company has a total cost function TC = 80+3q+2q2 and a marginal cost function MC = 3+4q. If market price is P = $30 and it is producing 10 units:(a) Is firm maximizing its profits?b) What quantity should it produce in long run? Hint: MC= ATCc) Construct a table with all costs.d) Plot profit maximization points in short and long run.
Assume a firm's short-run cost function is given by the following expression: C(q) = 2+q+q2 If the firm can sell each unit of their output at a price of p=9 dollars, what is the maximum profit the firm can earn in the short-run? a.) Maximum Profit = ? dollars
A firm has the following production function: q = 8KL, where q is the weekly output, K is the number of machines and L is the number of workers. Each machine rents for $50,000 per week and each worker costs $2,000 per week. The total cost includes the cost of machines and labor, as well as an additional $5,000 per unit of output for raw materials. The firm currently runs a single factory with 10 machines. Assume that capital is fixed in the short run. (a) How many workers are needed to produce 2,000 units of output per week (in the short run)? (b) How much does it cost to produce q units of output per week (in the short-run)? [The answer I expect is a particular function of q.
= Q5. A firm has the following fixed proportion production function q min(k, 21). a. Find the firms long-run total, average, and marginal cost functions. b. Suppose that k is fixed at 30 in the short run. Calculate the firms short-run total, average, and marginal cost functions. c. Suppose v = = 1 and w = 3. Calculate this firms long-run and short-run average and marginal cost curves.
b) Suppose a business faces a production function which is of the Cobb-Douglas form: Q(L,K) = AL“ Kß where Q represents total product, L represents labour units, K represents capital units, A is some fixed constant representing technology and a and B are fixed parameters. Show that if a + B> 1 there is increasing returns to scale. Also show that the output elasticities with respect to labour and capital are constants and equal to a and B, respectively.
a. A firm's long-run total cost can be written as LTC = 3000Q - 50Q2 + (1/3)Q3 and its long-run marginal cost by LMC = 3000 - 100Q + Q2. Find the range over which the firm will experience economies of scale. Explain your answer. b. A firm has a production function of Q = K * L + L, where the marginal product of labor is MPL = K + 1 and the marginal product of capital is MPK = L. The wage rate (W) is $100 per worker and the rental price (R) is $100 per unit of capital. In the short-run, capital (K) is fixed at 4. Find the minimum total cost of production in the short- and long-run if the firm produces 100 units of output.
Suppose a firm’s cost function is given by: C= 50 + 4q2 a) Find the equations for AFC, AVC and MC. b) If w=$4, what’s the short run production function for this firm?
A5
Full explanations would be appreciated! 25) In a short-run production process, the marginal cost is rising and the average variable cost is falling as output is increased. Thus, A) marginal cost is below average fixed cost. C) average fixed cost is constant. B) marginal cost is below average variable cost. D) marginal cost is above average variable cost. 26) A firm employs 100 workers at a wage rate of $10 per hour, and 50 units of capital at a rate of $21 per hour. The marginal product of labor is 3, and the marginal product of capital is 5. The firm A) could reduce the cost of producing its current output level by employing more labor and less capital. B) could reduce the cost of producing its current output level by employing more capital and less labor. C) could increase its output at no extra cost by employing more capital and less labor. D) is producing its current output level at the minimum cost. E) Both B and D are true.