MATH 235 Final: MATH 235 UMass Amherst spring01-final
Document Summary
Question 1 utility is quasilinear, i. e. , u(x) = v(x1) + x2. 20 4p1 = x1 implies p1 = 5 (1/4)x1. Hence, v (x1) = 5 (1/4)x1, and therefore v(x1) = 5x1 (1/8)x2: thus, u(x1, x2) = 5x1 (1/8)x2. Question 2 to produce q units of output, we must have z1 + 2z2 = q2. Thus, costs are c(w, q) = min{w1, 0. 5w2}q2. The rst order conditions for pro t maximization is p = min{w1, 0. 5w2}2q. Then the rm"s pro t function is (w1, w2, p) = p2. Question 3 suppose that a rm can operate at two locations, using one input at each location (the input also has the same price at the two locations). The production functions at the two locations are given by f (z) and g(z). Further, suppose that f has constant returns to scale and that g is strictly concave (and has therefore decreasing returns to scale).
