Question

PA 6. A parent has two children living in cities with different costs of living. The cost of living in city B is 3 times the cost of living in city A. The child in city A has an income of $2,000 and the child in city B has an income of $6,000. The parent wants to give a total of $2,000 to her two children. Her utility function is U(CA, CB)-CACB,where C A and C B are the consumptions of the children living in cities A and B respectively. She will choose to give 0096 each child $1,000, eventhough this will buy less goods for the child in city B. b. the child in city B 3 times as much money as the child in city A. c. the child in city B 1.50 times as much money as the child in city A d. the child in city A 3 times as much money as the child in city B. e. the child in city A 1.50 times as much money as the child in city B.

Answer 1

The correct answer is first option that is a) each child $1000, even though this will buy less goods for the child in city B.

As the parent has to maximize the utility which is the product of consumption of both the children. The total amount is 2000 so this can be taken as

Maximize U(x,y) = x.y

Subject to x +y =2000

Where x is consumption in the city A and y is consumption in city B. Which will be maximised at the level where the amount is given equally as 1000.