Answer to Question #265192 in Microeconomics for umair

Question

Suppose u = x1^1/2 x2^1/2 Initially we have p1 = p2 =1. but then p1 rises to 2. The consumer’s income is $40

a) . Solve for the optimal points both pre and post price change and show these point on a clear complete graph.

b) Define in words what the CV associated with this price change represents for this consumer. Using the method covered in class, solve for the CV associated with this price change for this consumer. Show this on a graph.

c) Define in words what the EV associated with this price change represents for this consumer. Solve for the EV associated with this price change for this consumer. Show this on a graph.

d) Which measure of welfare change is larger? Why?

Answer 1

(a)

At the optimal bundle $(x_2^*,x_1^*)$ , to fulfill budget exhaustion condition,

$P_1x_1^*+P_2x_2^*=m$

$x_2^*=(\frac{P_1}{P_2})x_1^*$

Optimal level for good 1:

$P_1x_1^*+P_2(\frac{P_1}{P_2})x_1^*=m$

$P_1x_1^*+P_1x_1^*=m$

$2P_1x_1^*=m$

$x_1^*=\frac{m}{2P_1}$

Optimal level for good 2:

$x_2^*=(\frac{P_1}{P_2})x_1^*$

(b)

The CV associated with this price change represents the maximum a consumer is willing to oay in order to have the economic change happening. In case of a negative economic change, CV is the minimum that the consumer needs in order to accept the economic change.

(c)

EV associated with this price change represents a measure of economic welfare changes . It is a representation of change in wealth at the current prices, that would have the same effect on the welfare of the consumer as it would for the change in prices with income unchanged.

(d)

CV is the measure of welfare that is larger. This is because a rise in price of a commodity implies that EV will be less than CV.