A firm with the production function f(x) = x₁x₂ wants to produce 100 units of output. a. How much of each input should the firm use if each unit of input costs $1? b. How much of each input should the firm use if w₁ = $1 and w₂ = $4? C. How much of each input will the firm need if it wants to produce 225 units of output and the price of each input is $1? d. Can you tell what kind of returns to scale this production function has from the input demands for each quantity of output?

A firm with the production function f(x) = x₁x₂ wants to produce 100 units of output. a. How much of each input should the firm use if each unit of input costs $1? b. How much of each input should the firm use if w₁ = $1 and w₂ = $4? C. How much of each input will the firm need if it wants to produce 225 units of output and the price of each input is $1? d. Can you tell what kind of returns to scale this production function has from the input demands for each quantity of output?

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

Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The marginal products associated with this production function are as follows: MPL = KM, MPK = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials.a) Suppose that the firm is required to produce Q units of output. Show how the cost - minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of capital depends on the quantity Q. Show how the cost - minimizing quantity of materials depends on the quantity Q. b) Find the equation of the firms long-run total cost curve.c) Find the equation of the firms long-run average cost curve.d) Suppose that the firm is required to produce Q units of output, but that its capital is fixed at a quantity of 50 units (ie., K 50). Show how the cost- minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of materials depends on the quantity Q. e)…
The manager of a T-shirt stand found that the cost to produce 10 T-shirts is $105.68, while the cost to produce 40 T-shirts is $402.98. Assume the cost C(x) is a linear function of x, the number of T-shirts produced. Calculate the marginal cost of a T-shirt, that is, the change in cost of producing one additional T-shirt. (Round to 2 decimal places)
1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form where A and n are positive constants. 3. The demand and total cost functions of a good arerespectively and a) Find expressions for TR, (profit) , MR, and MC in terms of Q. b) Solve the equation and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢1/4 million per floor (c) Specialized costs of GH¢10000x per floor. How many floors should the office complex contain if the average cost per floor is to be minimized? 5. The supply…
Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25 x2^0.5 Assume the price of input 1 is r and the price of input 2 is w. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?
Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels. Q = 1 Tech. K L A B Q=2 K L 2 4 1 6 1 3 2 5 Total Cost L K Assuming that the price of labor (P₁) is $1 and the price of capital (PK) is $3, calculate the total cost of production for each of the five levels of output using the optimal (least-cost) technology at each level. Q=3 K L 4 9 4 8 To do this, complete the table below by calculating the total cost of production, filling in the missing values using the optimal (least-cost) technology at each level. (Enter your responses as whole numbers.) Q=4 K L 12 5 Total Cost How many labor hours (units of labor) would be employed at each level of output? How many machine hours (units of capital)? To answer this, complete the table below for the units of labor and units of capital that would be used to produce each level of output. (Enter your…
Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels. Q = 1 Tech. K L A 4 1 B 1 3 Total Cost Q = 2 K L 2 5 6 2 Q=1 $6 L K Q = 3 Assuming that the price of labor (PL) is $2 and the price of capital (PK) is $1, calculate the total cost of production for each of the five levels of output using the optimal (least-cost) technology at each level. K 9 4 Q = 4 L K L 4 12 7 11 8 8 5 12 7 15 To do this, complete the table below by calculating the total cost of production, filling in the missing values using the optimal (least-cost) technology at each level. (Enter your responses as whole numbers.) Q = 5 $27 Q=2 $ 10 Q = 5 K L Q = 3 $ 17 Q = 4 $ 26 How many labor hours (units of labor) would be employed at each level of output? How many machine hours (units of capital)? To answer this, complete the table below for the units of labor and units of capital that…
Suppose that the market for microwave ovens is a competitive market. The following graph shows the daily cost curves of a firm operating in this market. 100 90 80 ATC 70 60 50 40 30 AVC 20 10 MC 5 10 15 20 25 30 35 40 45 50 QUANTITY (Thousands of ovens) For each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the graph to identify its total variable cost. Assume that if the firm is indifferent between producing and shutting down, it will produce. (Hint: You can select the purple points [diamond symbols] on the graph to see precise information on average variable cost.) Price Quantity Total Revenue Fixed Cost Variable Cost Profit (Dollars per oven) (Ovens) (Dollars) (Dollars) (Dollars) (Dollars) 25.00 1,600,000 70.00 1,600,000 $25.00 100.00 1,600,000 $35.00 If the firm shuts down, it must incur its fixed costs (FC) in the short run. In this case, the firm's…
2. A firm combines two inputs 21 and 22 to produce an output y. The prices of the two inputs are wi and w2, while the price of output is p. To produce an amount of output equal to y, the firm spends the following amount (which depends on the input prices): () () 248 + . Is it possible that the firm is minimizing cost when producing q? Explain C (w₁, W2, y) = (y) ats 48 A (w₁) ars. (W₂) a+s . If the answer to the previous question is positive, can you compute the conditional input demand functions? • How do your previous answers change if w₁ and we simultaneously double?
Suppose a firm is currently maximizing profit by producing 100 units of output per day. It is then discovered that the firm owes $1,000 for a one-time tax violation that occurred a few years ago. The firm now needs to pay the $1,000 to the government no matter what. How should the firm react to this additional cost? The firm should increase output in order to increase revenue enough to cover the additional cost. The firm should continue to produce 100 units of output per day, as the $1,000 is a sunk cost and therefore has no effect on production decisions. The firm should shut down in the short run and start back up in the long run. The firm should decrease output in order to decrease variable costs by $1,000.
a.)Suppose that labor is the only variable input in the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labor?b.)What are economies of scale? What are economies of scope? What is the difference between the two?
3. Optimal inputs: A firm has a production function, y = ln(l, k) in a market with prices Py = 20, pe = 4, Pk = 5. Find the firm's profit maximizing choice for y, l, and k. How much profit do they earn?
Consider the following marginal cost function MC= 5 + 2qi. (a) Does the production process exhibits increasing returns? decreasing returns? constant returns? (b) If the price is $23. What’s the optimal production level? (c) If the price is $31. What’s the optimal production level?