Suppose a caffeine-deprived man needs to wake up. Suppose his preferences on a d

Question

Suppose a caffeine-deprived man needs to wake up. Suppose his preferences on a day can be described by U=3*coffee+2*tea. If the price of coffee is $4 and the price of tea is $1. He has $12 to spend on these drinks on a day.
A. Find his utility for the following consumption combinations:
3 coffee, 0 tea.
1 coffee, 3 tea.
2 coffee, 1.5 tea.
0 coffee, 4.5 tea.
0 coffee, 12 tea.
4 coffee, 6 tea.
8 coffee, 0 tea.
B. Show his budget constraint, indifference curves, and optimal consumption choice in a graph. Use the horizontal axis for coffee and vertical axis for tea.
C. How many cups of coffee does he drink? How many cups of tea? What is his utility?

Explanation / Answer

A.

Utility = 3 × coffee + 2 × tea

For 3 coffee, 0 tea:

Utility = 3 × coffee + 2 × tea

            = 3 × $4 + 0

            = $12

For 1 coffee, 3 tea:

Utility = 3 × coffee + 2 × tea

            = 1 × $4 + 3 × $1

            = $7

For 2 coffee, 1.5 tea:

Utility = 3 × coffee + 2 × tea

            = 2 × $4 + 1.5 × $1

            = $9.5

For 0 coffee, 4.5 tea:

Utility = 3 × coffee + 2 × tea

            = 0 × $4 + 4.5 × $1

            = $4.5

For 0 coffee, 12 tea:

Utility = 3 × coffee + 2 × tea

            = 0 × $4 + 12 × $1

            = $12

For 4 coffee, 6 tea:

Utility = 3 × coffee + 2 × tea

            = 4 × $4 + 6 × $1

            = $20

For 8 coffee, 0 tea:

Utility = 3 × coffee + 2 × tea

            = 8 × $4 + 0 × $1

            = $32

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