Unformatted text preview: prices. Use this to prove that the cost function is non-decreasing in prices. 5. Consider a ﬁrm with the cost function c ( y,w 1 ,w 2 ) = y 2 ( w 1 + w 2 ) , where w i denotes the price of input i,i = 1 , 2 . Let p denote the output price. Derive the output supply function y ( p,w 1 ,w 2 ), and the input de-mand functions x i ( p,w 1 ,w 2 ) ,i = 1 , 2. 6. Consider a ﬁrm with production function y = ( x ρ 1 + x ρ 2 ) α , where 0 < ρ < 1 , and α > 0. For what value of ρ and α are there (i) increasing returns to scale; (ii) constant return to scales; (iii) decreasing returns to scale? Suppose that there are decreasing return to scale. Find the long run cost function. Derive the output supply function and the input demand functions. 1...
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- Fall '09
- Economics, input demand functions, output supply function, Dmitry Shapiro