Question

A consumer spends his entire monthly income on x and y. The price of a unit of x is $16 and the price of a unit of y is $12. If he consumes the bundle (x, y) = (40, 30), his MRS x for y is 3/2, meaning he would be indifferent to giving up 3 units of y to get 2 more units of x (or vice versa). Is this consumption plan optimal? If not, does the plan consumer include too much x or too much y? Depict this situation in a consumption diagram

Answer 1

Here MRS = 3/2 = 1.5

Price Ratio = Px/Py = 16/12 = 4/3 =1.33

Here MRS> Price Ratio.

This means that Consumer is willing to sacrifice more of Y to obtain X than the market requires him to. Here the Marginal utility that he obtains from X is 1.5 times of Y and costs him only 1.33 times of Y. Therefore the consumer will Consume more of X to reach the optimal bundle so that MRS decreases to be equal to Price Ratio.

Hence for the given Consumption bundle there's too much of Y.

In the above graph, blue line is the budget line, 16x+12y=1000

And red one shows one of the possible indifference curve for given MRS. (40,30) has been indicated.

For the given straight line preference relationship, it is clear that if the Consumer starts consuming only x =62.5, then he will be at a higher utility curve than given and shown in red. Hence there is too much y.

Hence it's not optimal Consumption plan.