Question

4. Suppose we have a market for coffee and pastries.

a. Graph the market (no need to give numbers for endpoints of the budget constraint) and show an optimal consumption bundle.

b. Suppose the price of coffee drops. Graph the new budget constraint.

c. Now, illustrate the INCOME and SUBSTITUTE effects of the price change and show the new optimum. Remember, you must draw the imaginary budget constraint and then find the tangency on the new budget constraint.

Answer 1

a. Suppose we measure coffee along the horizontal axis and pastries along the vertical axis. The initial budget line is AB and the initial indifference curve IC1 which is tangent to AB at point M with respect to which the initial consumption of coffee is q1 and initial consumption of pastries is X1. Now when the price of coffee drops, the budget line will rotate outward from AB to AC which becomes tangent to the new indifference curve IC2 at point O with respect to which the final consumption bundle is (q3,X3).

b. Now the total effect of increase in the consumption of coffee from q1 to q3 can be decomposed into a substitution effect and an income effect.
To understand the substitution effect, we will hold consumer's real income constant. Hence the consumer will stay on the same indifference curve IC1 but as the price of coffee drops, the price ratio has changed and thus the consumer will stay on the budget line with the slope equal to the slope of the new budget line. Hence we draw a hypothetical budget line DE which is tangent to the initial indifference curve IC1 at point N and is parallel to the new budget line AC. Hence the movement from point M to point N along which the consumption of coffee increases from q1 to q3 and the consumption of pastries decline from X1 to X2 is due to the substitution effect. As the price of coffee drops, consumer substitutes pastries with coffee.
Now to understand the income effect, we will consider real income as variable. Now as the price of coffee drops, consumer's real income or purchasing power M/p increases where M= income level and P= price level. Hence as consumer's purchasing power increases, consumer will feel richer and the budget line will shift rightward from DE to AC and the new budget line will become tangent to the new indifference curve IC2 at point O with respect to which the consumption of coffee is q3 and consumption of pastries is X3. Hence the movement from point N to point O along which the consumption of coffee increases from q1 to q3 and consumption of pastries increases from X2 to X3 is due to the income effect.