Question

A Californian student consumes Internet services (I) and books (B). Her preferences are represented by a Cobb-Douglas utility function: U(I,B) = I1/4B1/4 The prices of each good is $2 and the student has an income of $200. Over the course of the past year, the price of internet services has risen to $4, but the price of books has remained the same. The government has decided provide this student with additional money to compensate for the higher price of internet services. In order to determine the transfer the government has two consultants who have made the following suggestions:

Consultant A: The student’s income should be increased by a percentage found using a consumer price index (CPI).

Consultant B: The additional income should allow the student to get her initial level of utility.

1. (a) Find the consumer’s optimal bundle before the increase in price occurs.

2. (b) Find the consumer’s optimal bundle after the increase in price occurs with income still at $200.

3. (c) Find the amount of the transfer implied by consultant A.

4. (d) Is the student necessarily better or worse o↵ than before from such a transfer implied by consultant A? Explain why.

5. (e) Is the transfer implied by consultant B more or less than the amount implied by A? Explain. What is the precise dollar amount implied by consultant B?

Answer 1

Refer to the below images for the solution :

(d) With the transfer as implied by consultant , the budget line of the student shifts parallely outwards and the student's purcahsing power incraeses. Due to higher paying potential, the consumer is able to move on a higher indifferemce curve with a higher optimal consumptiin bundle. This is verified below:

The student is better off now because : C3 (500,100) > C2 (25,50)