Consider the following variation of the aggregate production function. Now firms must use oil M to produce output (in addition to labor and capital). The price of a unit of oil is p П max 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 production function exhibits constant returns to scale? (c) If the price of oil p rises, what would you expect to happen to carbon intensity (the ratio of oil per unit output: M/Y) in this economy? What happens to the revenue share of oil (the ratio of total oil payments to output: pM/Y)?
Consider the following variation of the aggregate production function. Now firms must use oil M to produce output (in addition to labor and capital). The price of a unit of oil is p П max 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 production function exhibits constant returns to scale? (c) If the price of oil p rises, what would you expect to happen to carbon intensity (the ratio of oil per unit output: M/Y) in this economy? What happens to the revenue share of oil (the ratio of total oil payments to output: pM/Y)?
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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Transcribed Image Text:Consider the following variation of the aggregate production function. Now
firms must use oil M to produce output (in addition to labor and capital). The
price of a unit of oil is p
П
max 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 production
function exhibits constant returns to scale?
(c) If the price of oil p rises, what would you expect to happen to carbon
intensity (the ratio of oil per unit output: M/Y) in this economy? What
happens to the revenue share of oil (the ratio of total oil payments to
output: pM/Y)?
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