Question

4. (25p) Mr. Novak's utility function is Ufa, y) = min{a,y} and his income is M = 200. He currently lives in a city in which the prices of goods x and y are both equal to 1. Mr. Novak's boss is thinking of sending him to another town, where the prices of the two goods are p = 1 and Py = 4. The boss offers no pay raise. Mr. Novak complains, saying that having to move is equivalent to a pay cut of A. He says he would be willing to move if he got a raise of at least) B. Compute A and B.

Answer 1

In such type of utility function, utility is maximized if x=y.

In first case, budget constraint is given by

x*px+y*py=M

1*x+1*y=200

x+y=200

put x=y

y+y=200

y=100

So, x=y=100

Currently Novak will consume 100 units of x and 100 units of y.

Let us see if px=1, py=4

budget constraint is given by

x*px+y*py=M

1*x+4*y=200

x+4y=200

put x=y

y+4y=200

y=40

So, x=y=40

Equivalent amount of income it Novak consumes the above combination before transfer,

M=1*40+1*40=$80

Equivalent salary cut=A=200-80=$120

Novak will be ready to move to another town if he is able to maintain the same level of utility i.e. same level of consumption. Income required to maintain same level of consumption in new town is

Income required=1*100+4*100=$500

Raise in salary required=B=500-200=$300