Charlie has a repair shop that uses three inputs: Unskilled Labor (quantities of which will be denoted by L), Skilled Labor (H) and Machinery (K). The inputs (L, H, K) produce: y = LAHK units of repairs. Charlie is a price-taker in all markets. The wages of unskilled and skilled labor are w₁ and wд respectively, and the running cost of K units of machinery is wk. Charlie's repair shop is equipped with K = 1 unit of machinery, which cannot be adjusted. To produce any positive output all the machinery in the repair shop must be turned on, but if no output is produced he can choose not to turn on the machinery. There is no upper limit on the output of Charlie's repair shop. He is a profit maximizer, and hence for any level of output y he will adjust (L, H) to minimize cost. Input prices are (WL, WH, WK) = (1,2,27). (a) Derive Charlie's short-run cost function sc(wL, WH, WK, y, K), and then specialize it to the given input prices. Determine the cost-minimizing ratio: are of unskilled to skilled labor. L(WL, WH, WK,Y, K) H(WL, WH, WK, y, K) (b) Let the output price be p. What is Charlie's optimal output and profit as a function of p? 1 as downloaded by 100000834378767 from CourseHero.com on 10-13-2021 09:21:20 GMT -05:00 ero.com/file/59278065/EC-501-Practice-midterm-2020pdf/ (c) Consider the following model of long-run competition. Repair shops of the kind described above can freely enter and exit the market, each furnished with K = 1; but there are no repair shops with higher or lower levels of K. What is the price p in the long-run equilibrium? How much does each repair shop produce? Find how many repair shops will be operating in the long-run equilibrium if the market demand curve is: p+Y=1050.
Charlie has a repair shop that uses three inputs: Unskilled Labor (quantities of which will be denoted by L), Skilled Labor (H) and Machinery (K). The inputs (L, H, K) produce: y = LAHK units of repairs. Charlie is a price-taker in all markets. The wages of unskilled and skilled labor are w₁ and wд respectively, and the running cost of K units of machinery is wk. Charlie's repair shop is equipped with K = 1 unit of machinery, which cannot be adjusted. To produce any positive output all the machinery in the repair shop must be turned on, but if no output is produced he can choose not to turn on the machinery. There is no upper limit on the output of Charlie's repair shop. He is a profit maximizer, and hence for any level of output y he will adjust (L, H) to minimize cost. Input prices are (WL, WH, WK) = (1,2,27). (a) Derive Charlie's short-run cost function sc(wL, WH, WK, y, K), and then specialize it to the given input prices. Determine the cost-minimizing ratio: are of unskilled to skilled labor. L(WL, WH, WK,Y, K) H(WL, WH, WK, y, K) (b) Let the output price be p. What is Charlie's optimal output and profit as a function of p? 1 as downloaded by 100000834378767 from CourseHero.com on 10-13-2021 09:21:20 GMT -05:00 ero.com/file/59278065/EC-501-Practice-midterm-2020pdf/ (c) Consider the following model of long-run competition. Repair shops of the kind described above can freely enter and exit the market, each furnished with K = 1; but there are no repair shops with higher or lower levels of K. What is the price p in the long-run equilibrium? How much does each repair shop produce? Find how many repair shops will be operating in the long-run equilibrium if the market demand curve is: p+Y=1050.
Chapter11: The Firm: Production And Costs
Section: Chapter Questions
Problem 15P
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Transcribed Image Text:Charlie has a repair shop that uses three inputs: Unskilled Labor (quantities of which
will be denoted by L), Skilled Labor (H) and Machinery (K). The inputs (L, H, K)
produce:
y =
units of repairs. Charlie is a price-taker in all markets. The wages of unskilled and
skilled labor are w̟ and wy respectively, and the running cost of K units of machinery
is wK. Charlie's repair shop is equipped with K = 1 unit of machinery, which cannot
be adjusted. To produce any positive output all the machinery in the repair shop must
be turned on, but if no output is produced he can choose not to turn on the machinery.
There is no upper limit on the output of Charlie's repair shop. He is a profit maximizer,
and hence for any level of output y he will adjust (L, H) to minimize cost. Input prices
are (wL, Wн, Wк) —D
(1, 2, 27).
(a) Derive Charlie's short-run cost function sc(wL, WH, WK, Y, K), and then specialize
it to the given input prices. Determine the cost-minimizing ratio:
L(WL, Wн,Wк,у, К)
Н (WL,WH,Wк,У, К)
of unskilled to skilled labor.
(b) Let the output price be p. What is Charlie's optimal output and profit as a
function of p?
harewia
1
as downloaded by 100000834378767 from CourseHero.com on 10-13-2021 09:21:20 GMT -05:00
ero.com/file/59278065/EC-501-Practice-midterm-2020pdf/
(c) Consider the following model of long-run competition. Repair shops of the kind
described above can freely enter and exit the market, each furnished with K = 1;
but there are no repair shops with higher or lower levels of K. What is the price
p in the long-run equilibrium? How much does each repair shop produce? Find
how many repair shops will be operating in the long-run equilibrium if the market
demand curve is:
p+Y = 1050.
He
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