Jill has a utility function defined on two goods x1 and x2 J

Jill has a utility function defined on two goods: x_1 and x_2. Jill\'s utility function is of the form i u(x_1,x_2) = 2 x_1^1/2 x_2^1/2. Her budget constraints are of the form 10 = x_1 + 2x_2 10 = 2x_1 + x_2 What would happen if her budget constraint became 30 = x_1 + 2x_2 10 = 2x_1 + x_2.

Solution

When budget constraint was

10 = x1+2x2 and

10 = 2x1 + x2

It meant that prices of X1 and X2 were same.

But if it changes to

30 = x1+2x2 and

10 = 2x1 + x2

It means price of X2 is more than X1

In this case, since utility being derived from two goods is same as given from utility function (it is a Cobb Douglas production function with equal marginal utilities) he will buy more of x1. He will substitue X1 for X2.