Consider the problem of a consumer that has to decide how mu

Consider the problem of a consumer that has to decide how much to consume of goods x and y. He derives a benefit of 2*square root of x from consuming x units of the first good, and a benefit of 4*square root of y from consuming y units of the second good. Each unit of x costs $10. Each unit of y costs $5. The consumer wants to spend a total of $90 0n both goods.

QUESTION. How many units of y does he buy at the optimal bundle?

Solution

A consumer tries to equate his MRS with price ratio to maximise his satisfaction.Thus at equilibrium point

MU_X / MU_y = 10/5

2 * 1/2 * x^-1/2 / 4 * 1/2 * y^-1/2 = 2

Solving we get y = 16x

Now given income of individual = 90 we have

10x + 5y = 90

10x + 5 * 16x = 90

90x = 90

x = 1.

Thus y =16 * 1 = 16 units.Thus optimal bundle comprises of 16 units of y.