Problem 1LK² and faces a wageA soap manufacturer has the production function q =rate of $45 and rental rate of capital of $90.(a)Find the cost-minimizing ratio of capital to labor. (This is alsocalled the output expansion path).(b)Suppose the firm plans to produce q=1,000. Determine the cost-minimizing amount of labor and capital.(c)How much will it cost to produce q=1,000 (long run)?Suppose the firm decides to increase its output to q = 1331, but isunable to increase its quantity of capital from the amount in b. Howmuch labor will the firm need to employ and what will be the costof producing q = 1331?(d)(e)If the firm continues to produce q = 1331 over a long period of time,how will it alter its capital and labor from part d.? What will it costto produce q = 1331 in the long run?On a graph, draw the two isoquants from above and the isocostlines corresponding to the LR and SR costs (there should be three).Identify the optimal L and K for each part on the graph.(f)

“Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

A soap manufacturer has the production function q = LK² and faces a wage rate of $45 and rental rate of capital of $90. (a) Find the cost-minimizing ratio of capital to labor. (This is also called the output expansion path). (b) Suppose the firm plans to produce q=1,000. Determine the cost- minimizing amount of labor and capital. (c) How much will it cost to produce q=1,000 (long run)?

A soap manufacturer has the production function q = LK² and faces a wage rate of $45 and rental rate of capital of $90. (a) Find the cost-minimizing ratio of capital to labor. (This is also called the output expansion path). (b) Suppose the firm plans to produce q=1,000. Determine the cost- minimizing amount of labor and capital. (c) How much will it cost to produce q=1,000 (long run)?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

The cost (C) of a apples in dollars can be represented by the function C(a)=0.27a, and the cost (P) in dollars of b bananas can be represented by the function P(b)=kb, where k is a constant. If C(10)+P(8)=$5.34, what is k ?
The total revenue function for a product is given by R=655x dollars, and the total cost function for this same product is given by C=19,250+70x+x2, where C is measured in dollars. For both functions, the input x is the number of units produced and sold. a. Form the profit function for this product from the two given functions. b. What is the profit when 25 units are produced and sold? c. What is the profit when 43 units are produced and sold?
Q2. Determine the returns to scale of the following production function: Y = 5K0.5 +3L0.5 (a) constant (b) increasing (c) decreasing (d) indeterminate
The production function for a product is given by q = 100KL. If the price of capital is $120 per day and the price of labor $30 per day, what is the minimum cost of producing 1000 units of output?
For the given cost function C(x) = 40000 + 700x + x² find: a) The cost at the production level 1700 b) The average cost at the production level 1700 c) The marginal cost at the production level 1700 d) The production level that will minimize the average cost e) The minimal average cost
A typical firm in industry X has the following total cost function: TC = 400 + 38*q + 0.5*q2, where q represents the units of output. • This firm is producing 35 units of output and the firm's MC(q=35) = $73 and AC(q=35) = $66.9. (a) At this level of output, the firm's AC(q) function is in output (q). (Enter just one word: increasing or decreasing). (b) The firm faces of scale. (Enter just one word: economies or diseconomies.).
Assume that it costs a company approximately C(x) = 400,000 + 180x + 0.001x² dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) C(10,000) $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.