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NEED DETAIL PLZ Leo thinks leisure (R) and consuming goods (C) are perfect complements. Goods cost...

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?

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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.

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