Question

6. (10 points) Utility. Suppose we have two cities, 1 and 2. Assume every individual has the same utility function given by: u(wj, rj) = W; – 0.5 *r; where j = 1 or j = 2. Furthermore, for all parts of the problem assume the total population is fixed at 1,008 and wages in each city are given by: W1 = 200 W2 = 110 (A) What is the utility from each choice if rı = 20 and r2 = 30. Is this an equilibrium? How do you know? (2 points)

Answer 1

U = wj -0.5rj

for city 1 total utility , U1 = 200 - 0.5* 20 = 200 - 10 = 190

for city 2, tota utility U2 = 110 - 0.5*30 = 110 - 15 = 95

total utility derived from each city by each individual is different.

In order to check equilibrium, marginal utility derived from each factor income need to check.

$\Delta u/\Delta w= (190-95)/(200-110) = 95/90= 1.056$

$\Delta u/\Delta r= (190-95)/(30-20) = 95/10= 9.5$

MUw$\neq$ MUr

Hence, in the given ware- rent framework, cities are not in equilibrium.