Consider the following variation of the aggregate production function. Nowfirms must use oil M to produce output (in addition to labor and capital). Theprice of a unit of oil is pПmax II = AK°L³M – wL-rK – pM(a) Find a first-order condition for the firm's demand for oil.(b) What must be true about the parameters a, B, and y if this productionfunction exhibits constant returns to scale?(c) If the price of oil p rises, what would you expect to happen to carbonintensity (the ratio of oil per unit output: M/Y) in this economy? Whathappens to the revenue share of oil (the ratio of total oil payments tooutput: pM/Y)?

a) To find the first-order condition for the firm's demand for oil, we take the derivative of the…

Answered: Consider the following variation of the…

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter21: Production And Costs

Section21.3: Production

Problem 3ST

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Sam Malone is considering renovating the bar stools at Cheers.The production function for new bar stools is given byq = 0.1k 0.2l0.8 where q is the number of bar stools produced during the renovation week, k represents the number of hours of bar stoollathes used during the week, and l represents the number ofworker hours employed during the period. Sam would like toprovide 10 new bar stools, and he has allocated a budget of$10,000 for the project.a. Sam reasons that because bar stool lathes and skilled barstool workers both cost the same amount ($50 per hour),he might as well hire these two inputs in equal amounts.If Sam proceeds in this way, how much of each input willhe hire and how much will the renovation project cost?b. Norm (who knows something about bar stools) arguesthat once again Sam has forgotten his microeconomics.He asserts that Sam should choose quantities of inputs sothat their marginal (not average) productivities are equal.If Sam opts for this plan instead, how much of…
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Under what conditions do the following production functions exhibit decreasing, constant, or increasing returns to scale? a) q=L+K b) q=LaKb c) q= L+ LaKb + K
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Consider the following production function with inputs L and K: Q = (L 0.5 + K0.5)2. The input prices are r = 2 and w = 1. 1) What is the optimal use of labor and capital? 2) Consider a technological advacement such that Q = 2(L 0.5 + K0.5)2 and w = r = 1. What is the optial level of K and L? Any change in K/L? What is the new cost?
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