Victor is the manager of a local bank branch in College Station where he consume

Question

Victor is the manager of a local bank branch in College Station where he consumes bundles of two commodities x and y. Prices in College Station are px=1 and py=5. He is offered a transfer to Dallas where prices are px=2 and py=8; Victor’s utility function is U(x,y)=xy and his income in College Station is $5000. (Victor’s utility maximization is always characterized by the tangency rule). Will Victor be able to afford what he was buying in College Station if he is offered a salary in Dallas that guarantees his welfare is the same with the transfer?

No.

Yes.

Explanation / Answer

Yes, he will be able to afford what he was purchasing earlier after the transfer if his welfare remains the same. This is because the salary is increased such that his utility remains the same in Dallas as they were in college station.

For utility maximization, the marginal rate of substitution of x for y (MRS) is equal to the price ratio.

U = xy

Marginal utility of x = dU/dx = y

Marginal utility of y = dU/dy = x

MRS(x,y) = y/x

At equilibrium , y/x = p(x) / p(y)

In college street, p(x) = 1 and p(y) = 5

So, y/x = 1/5 or x = 5y

The budget constraint is given by ,

x* p(x) + y* p(y) = Income or x*1 + y*5 = 5000 or 5y*1 + y*5 = 5000 (putting x = 5y) or 10 y = 5000 or y = 500

x = 5*500 = 2500

So, before transfer he used to consume 2500 units of x and 500 units of y.

Even after the transfer, he will consume the same amounts of x and y in order too keep the utility U= xy constant.

Therefore, now his income should be increased such that he can now consume 2500 units of x at $2 per unit and 500 units of y at $8 per unit. Putting these in this budget constraint, we get

Income after transfer = 2*2500 + 8*500 = 9000

Therefore, in order to maintain his welfare as the same as before transfer his income will increase to $9000. At this income he will be able to purchase the same basket of goods that he used to consume before.

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