1.) Production, Inputs, and Cost: Building Blocks for Supply Analysis The firm can generally substitute one input for another. Whether or not it pays to substitute depends on the relative costs of labor and machinery. First, describe the alternative types of input proportions available to the firm. Then, describe the combination of inputs that represent the least costly way for the firm to produce its goods. Lastly, give one example of the firm’s substitutability from a recent news article.

1.) Production, Inputs, and Cost: Building Blocks for Supply Analysis The firm can generally substitute one input for another. Whether or not it pays to substitute depends on the relative costs of labor and machinery. First, describe the alternative types of input proportions available to the firm. Then, describe the combination of inputs that represent the least costly way for the firm to produce its goods. Lastly, give one example of the firm’s substitutability from a recent news article.

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter30: Market Failure: Externalities, Public Goods, And Asymmetric Information

Section30.2: Internalizing Externalities

Problem 2ST

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3. The production function for diapers is: q = 6L12 K2 Where q is the number of diapers produced, L is labor hours, and K is machine hours. Assume that the firm can use part of an hour of capital and part of an hour of labor. а) If the diaper firm wants to produce q = 60, what combination of L and K would it use if the rental rate of capital= Pg = $4/hour and the wage rate of labor = P, = $2/hour? 2 b) If the diaper firm continues to produce q = 60, what combination of L and K would the firm use if Pg stayed the same, but P, increased to $4/hour? If P, = $4 and P = $4, how much K and L would the diaper firm use to produce 36 diapers? 30 diapers? d) Using your answers to (b) and (c) graph the long-run average cost curve for the firm.
3. Consider the delivery of mail. In general, what is the shape of the average total cost curve? How might the shape differ between isolated rural areas and densely populated urban areas? How might the shape have changed over time? Explain.
Economics Question
3. Optimal use of multiple inputs. In his shop, Jim Valenti retrofits sunroofs into automobiles. The process can use a combination of skilled labor and unskilled labor. Given his current mix of employees, the marginal product of the last unit of skilled labor is 4 sunroofs per day, and the marginal product of the last unit of unskilled labor is 1 sunroof per day. Current market rates for skilled and unskilled labor is $40 and $20, respectively. Is Julian using a least cost combination of inputs? If not, which of type of labor should he use relatively more? Comparison Expression: Result:
3) Ajax, Inc. assembles gadgets. It can make each gadget either by hand or with a special gadget- making machine. Each gadget can be assembled in 15 minutes by a worker or in 5 minutes by the machine. The firm can also assemble some of the gadgets by hand and some with machines. Both types of work are perfect substitutes, and they are the only inputs necessary to produce the gadgets. a) Write down the equation of the firm's production function for the firm. Let G be the number of gadgets assembled, M the number of hours the machines are used, and I the number of hours of labor. b) It costs the firm $30 per hour to use the machine and $10 per hour to hire a worker. The firm wants to produce 120 gadgets. What is the cost-minimizing input quantities? Illustrate your answer with a clearly labeled graph. d) Derive the expression for the long-run total cost that the firm incurs, as a function of q. Represent it in a diagram.
At an output level of 99, what is the cost minimizing combination of Labor and Kapital? At an output level of level of 154, what is the cost minimizing level of Labor and Kapital If the price of the product is $2.00, what is the profit maximizing combination of Labor and Kapital? What is the total profit?
PLEASE DO IT ASAP, DON'T COPY FROM CHEGG
2. 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?
I need help to see if I am doing this correctly, and I'm not sure how to plot and answer the last question. Thank you.
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5. The annual output for a luxury hotel chain is given by Q = 30K²/5 L¹/2 R¹/4, where K, L and R are the capital, labor and real estate inputs, all measured in $1,000,000 s, and Q is the average number of rooms rented per day. The hotel chain's annual budget is B = $69 million. (a) How should they allocate this budget to the three inputs in order to maximize their annual output? What is the maximum output? (b) What is the approximate change in the firm's maximum output if their annual budget increases by $500,000? Explain your answer.
2. Inputs and outputs Edison's Performance Pizza is a small restaurant in Philadelphia that sells gluten-free pizzas. Edison's very tiny kitchen has barely enough room for the three ovens in which his workers bake the pizzas. Edison signed a lease obligating him to pay the rent for the three ovens for the next year. Because of this, and because Edison's kitchen cannot fit more than three ovens, Edison cannot change the number of ovens he uses in his production of pizzas in the short run. However, Edison's decision regarding how many workers to use can vary from week to week because his workers tend to be students. Each Monday, Edison lets them know how many workers he needs for each day of the week. In the short run, these workers are inputs, and the ovens are inputs. Edison's daily production schedule is presented in the following table. Fill in the blanks to complete the Marginal Product of Labor column for each worker. Labor Output Marginal Product…