Question

NEED DETAIL PLZ

Leo thinks leisure (R) and consuming goods (C) are perfect complements. Goods cost $1 per unit. Leo wants to consume 5 units of goods per hour of leisure. Leo can work as much as he wants to at the wage rate of $15 an hour. He has no other source of income. One day has 24 hours.

a. What is his utility function and budget constraint?

b. How many hours a day will Leo choose to spend at leisure?

Answer 1

a) There are 24 hours in a day to be used for consuming goods and enjoying leisure. The two goods are perfect

complements implying that they are always used together at the rate of 5 units of goods per hour of leisure.

This gives C = 5R. If R is 1, then C becomes 5. This makes the utility function U (C, R) = min (C, 5R).

b) Now budget equation is Consumption = Income or C = (24 – R)*15.

This is because working hours are 24 – leisure hours. Now budget equation is C + 15R = 360.

Use C = 5R to get 5R + 15R = 360 or R = 360/20 = 18 hours and working hours = 24 – 18 = 6 hours.

Leisure hours are 18.