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{3M,C}. Coffee costs $2/oz, milk

2

$1/oz.

(a) (10 Points) How much coffee and how much milk will Boris buy per week?

(b) (10 Points) How much coffee and how much milk will Boris buy per week if the price of coffee rises to $6/oz?

(c) (5 Points) 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) This is a case of perfect complements. The consumer’s preferences are such that he prefers 3 parts of coffee for every 2 parts of milk. In other words, for every M units of milk, he prefers 1.5M units of coffee. That is,

            C = 1.5M        

The budget line is given by the following equation.

            PCC + PMM = 40

Since C = 1.5M and PM=1,

            PC(1.5M) + M = 40

This implies

            M = 40 / (1.5PC + 1)   

And C = 1.5M = 60 / (1.5PC + 1)

When PC = 2,

            C = 60 / (1.5(2) + 1) = 60/4 = 15

            M = 40 / (1.5(2) + 1) = 40/4 = 10

(b)

When PC = 6,

            C = 60 / (1.5(6) + 1) = 60/10 = 6

            M = 40 / (1.5(6) + 1) = 40/10 = 4

(c)

The following figure shows the impact of change in the price of coffee.

The original budget line is EF, and the original optimal bundle is A. As the price changes, the new budget line become EG, and the new optimal bundle is B.

Separating income and substitution effects:

To make the consumer able to purchase the old bundle, some income is given to him and the budget line becomes CD. The movement from the original bundle to the optimal bundle at budget line CD shows the substitution effect. But at budget line CD, the original bundle is not only affordable; it is also the optimal bundle. This means there is no substitution effect. And the complete price effect is the income effect.

In the case of perfect complements, the substitution effect is always zero.

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