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# economics Assignment

Question # 00000565
Subject: Economics
Due on: 09/10/2013
Posted On: 08/23/2013 04:06 PM

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Consider a single-product firm under monopoly. The firm's profit function is given by ? = PQ-wL-rK, where P=price, Q=output, L=labor, K=capital, w=wage, and r=rent.

Let the market demand function and the firm's production function be Q=PQ=P-2 and Q=K raised to the power (4/5)*L raised to the power (4/5), respectively.

(a) Is the production function homogeneous? If so, of what degree? Discuss the returns to scale for this function.
(b) Is the production concave? Is it quasiconcave? Show your work.
(c) Rewrite the profit function as a function of L and K. Is it homogeneous with respect to L & K? If so, of what degree?
(d) Is the profit function concave in L &K? Is it quasiconcave? Show your work.
(e) What would happen if this function pertained to a perfect competition instead of a monopoly?

Min Pages: 1
Level of Detail: Show all work
Other Requirements: Production Function: Q=K?4/5L?4/5

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#### economics Assignment

Tutorial # 00000442
Posted On: 08/23/2013 04:07 PM
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Tutorial Preview …Discuss xxx returns xx scale for xxxx function The xxxxxxxxxx function xx xxxxx by, xxxxxx = K4/5L4/5 xxxxxxx both inputs, xxxxxxx and xxxxx xxx scaled…
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single-product_firm.docx (18.17 KB)
Preview: for xxx function xx be quasiconcave xx require the xxxxxxx second xxxxx xxxxxxxxx minor xx be positive xxxxx the function xx not xxxxxxxxxxxx xxxxxxxxxxx it xxxxx sense that xxx function is xxxxxxx concave xxx xxxxxxxxxxxx since xx exhibits increasing xxxxxxx to scale xxx Rewrite xxx xxxxxx function xx a function xx L and x Is xx xxxxxxxxxxx with xxxxxxx to L xxxxx K? If xxx of xxxx xxxxxxxx = xxxxxxxx = [(Q+2)*Q] xxxxx –rK = xxxxxxxxxxxxxxxxxxxxxxxxx –wL xxx xx Therefore xxxxxx = = xxxxxxxxxxxxxxxxxxxxxxxxx –wL – xxxxx let xxxx xxxxxxx capital xxx labor are xxxxxx up (or xxxxxxxxxx by x xxxxxx factor x (lamda) ?(?L, xxx = {[(?K)4/5(?L)4/5)+2]*( xxxxxxxxxxxxxx –w(?L) xxx xxxxx = xxxxxxxxxxxxx + 2 xxxxxxxxxxxx – ?wL xxx ?rK xxxxxxxxx xxx function xx not homogenous xxxxx the scalar x cannot xx xxxxxxxx out xx the expression, x e when xxxx input xxxxxxx xxx changed xx the scalar xx the resulting xxxxxxxxxx is xxx xxxxxxxxxxxxxxxx or xxxxxxxxxx separable in xxxxx.....
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