Boris budgets $40/week for his morning coffee with milk. He likes it only if it

Question

Boris budgets $40/week for his morning coffee with milk. He likes it only if it is prepared with 3 parts coffee, 2 part milk U=min{3/2M, C}. Coffee costs $2/oz, milk $1/oz.

a.       How much coffee and how much milk will Boris buy per week?

b.      How much coffee and how much milk will Boris buy per week if the price of coffee rises to $6/oz?

c.       Graph the two budget constraints and the two optimal bundles with coffee on the x-axis. On the graph, show how much of the total change is due to the income effect? How much to the substitution effect?

Explanation / Answer

a. Let C = coffee (ounces/week) and M = milk (ounces/week). Because of Boris's preferences, 2C = 3M. At the original prices we have:

3/2M(2) + M(1) = 40

4M = 40

So M=10 and C=15

b. Let M' and C' be the new values of milk and coffee. Again, we know that 2C' = 3M'. With the new prices we have:

3/2M'(6) + M'(1) = 40

10M'=40

M'=4, C=6

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