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Question # 00000828
Subject: Economics
Due on: 09/17/2013
Posted On: 09/08/2013 10:42 AM

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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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Tutorial # 00000695
Posted On: 09/08/2013 10:45 AM
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mac123
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single-product_firm.docx (18.17 KB)
Preview: function xxxxxxxx increasing xxxxxxx to scale xxxx when both xxxxxx are xxxxxx xx by xxx same factor xx output, Q, xxxxxxxxx by x xxxxxx greater xxxx ? [=?1 xx Therefore the xxxxxx of xxxxxxxxxxx xx 1 x That is xxxx both inputs xxx scaled xx xx a xxxxxx of ?, xxxxxx increases by x factor xx x 6 xxxxx ? (b) xx the production xxxxxxxx Is xx xxxxxxxxxxxxx Show xxxx work A xxxxxxxx is concave xx its xxxxxxx xxxxxx is xxxxxxxx semidefinite, i x its principal xxxxxx alternate xx xxxxx starting xxxx negative sign xx e odd xxxx are xxxxxxxx xxx even xxxx positive) QL=dQ/dL x 4/5*(K4/5L-1/5) ; xxxxxxxx = xxxxxxxxxxxxxxxxxx x d2Q/dL2 x -4/25(K4/5L-6/5) ; xxx = d2Q/dK2 x -4/25(K--6/5))(L(4/5))QKL x xxxxxxxx = xxxxxxxxxxxxxxxxx ; QLK x d2Q/dKdL = xxxxxxxxxxxxxxxxxx = xxxxxxxxxxxx x -4/25(K45)(L-65)16/25(K-15)(L-15)16/25(K-15)(L-15)-4/25(L45)(K-65) xxx first principal xxxxx is QLL xxxxxxxxxxxxxxxxx ?0 xxx xxx K,L xxx second principal xxxxx is the xxxxxxx matrix xxxxxx xxx H x {[-4/25(K4/5L-6/5)]*[ -4/25(K--6/5))(L(4/5))]} xxx {[16/25(K-1/5L-1/5)]*[16/25(K-1/5L-1/5)]},i e xxx H x xxxxxxxxxxxxxxxxxxxx.....
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