ps4_2012 - Cornell University Spring 2012 Economics 3130...

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Cornell UniversitySpring 2012Economics 3130: Problem Set 4Due Friday, October 12, 2012 4PM1. For each of the following production functions: 1) determine whether whether theyexhibit increasing, decreasing or constant returns to scale, 2) determine whether thefunction is homogeneous of any degree, and 3) determine for each of the inputs whetherthere is an increasing, constant or decreasing marginal product.(a)f(l) = 2l-l.(b)f(k, l) =k1/2l1/2(c)f(k, l) = (l)1/2+k2. Question 12.3BThe following questions will not be graded.3. (Question 11.2B from text, modified) Suppose a firm has the production functionx=f(l) = 2l1/2(a) Find the firm’s input demand functionl(p, w).(b) Find the firm’s supply functionx(p, w).(c) Find the firm’s profit functionπ(p, w).(d) Find the firm’s cost functionc(w, x).(e) What is the firm’s marginal cost function? average cost function?(f) Confirm that you get the same supply function by settingp=MC. Check thatthe average cost condition holds.

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