ECN Test 2 (1)

# ECN Test 2(1) - Economics 505 MATHEMATICAL ECONOMICS EXPLAIN your answers carefully In-class part Please turn your cell phones off Spring 2005

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Economics 505 MATHEMATICAL ECONOMICS Spring, 2005 Test #2 EXPLAIN your answers carefully . In-class part. Please turn your cell phones off. 1. (20) A competitive firm with production function Q = (KL) seeks to maximize profit by á hiring non-negative amounts of K and L. Its output price is P and factor prices are r and w; those three parameters and á are all positive. Thus profits are given by ð (K,L) = P @ (KL) – rK – wL. á (A) (6) Show that if P > r+w and á > ½, no weak global maximum exists. (B) (7) For the case á < ½, find the weak global maximum. (C) (7) (Comparative statics) How does the solution value of K change when r increases? + 2. (20) Professor Gensemer has a utility function on o : 3 x for non-negative x, y, and z, which she wishes to maximize subject to the budget constraint: p x yz x y z , + p y + p z = I where income I and all prices, p , p and p are positive. What decision should Prof. Gensemer make? [Assume that a global maximum exists.] 3. (20) Your job is to design a least-cost cylindrical can for our crushed tomato product. The can will have height h and the top and bottom will be disks of radius r [both measured in inches].

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