Question

The price of a bottle of beer is $1 and the price of a pizza is $10. The MRS of bottles of beer for pizza expressed by Karl is 5. Has Karl chosen the optimal amount of beer? How do you know? If Karl is not maximizing, what should he do to improve his situation? (Hint: what is the MRS at the consumer optimum point?)

Answer 1

SOLUTION : The consumer is said to achieve maximum satisfation if and only if the following condition is met:

I.e MRS = Px/Py

which means Marginal rate of substitution is equal to price rate of the goods.

let us check whether this condition is met or not :

let us suppose that beer is Y-good and Pizza is X-good .

So the price ratio will be Px/Py = 10/1

Similary MRS= change in Y / change in X = 5/1 .THIS MEANS THE CONSUMER WILL GIVE UP 5 UNITS OF Y -GOOD FOR ONE UNIT OF X-GOOD.

If you see 5/1 is not equal to 10/1. So the consumer is not in equilibrium hence he is not able to choose the optimal amount of beer.

MUX /MUY = PX/PY

5/1 = 10/1

5/10 < 1/1

both are not equal .Here Margianl utility of Y per dollar is greater than the marginal utility of X per dollar. So we need to increase the quantity of good y so that the marginal utility of y-good per dollar will decrease and become equal to marginal utility of X good per dollar.

Margianl rate of substitution should be equal to 10/1 .