Question

Suppose Voodoo Donuts and Stumptown Coffee are perfect complements, consumed together one donut to one cup of coffee. Suppose the price of a donut is $1 and the price of a cup of coffee is $3. Use both graphs and words to explain income and substitution effects when the price of coffee to rise to $4.

Answer 1

Suppose Voodoo Donuts and Stumptown coffee are are perfect complements. Here the initial budget line is AB which becomes tangent to the initial L shaped indifference curve IC1 at the point of kink Eo with respect to which stumptown coffee and voodoo donuts are consumed in 1:1 ratio. Now when the price of coffee rises to $4, the budget line will rotate inward from AB to AC which becomes tangent to the new indifference curve IC2 at the point of kink E1 with respect to which the final consumption of stumpyown coffee and voodoo donuts are X3 and X4 respectively. Now the movement from Eo to E1 can be decomposed into a substitution effect and an income effect.
   To understand the substitution effect ,we will consider consumer's real income constant. Hence the consumer will stay on the same indifference curve IC1 but as the price ratio has changed due to an increase in the price of coffee. Hence the consumer will stay on the budget line with 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 E0 and is parallel to the new budget line AC. However the hypothetical budget line is tangent to the initial indifference curve at the same point I.e at point Eo. Hence here the substitution effect is zero as the consumer is still consuming at point E0 I.e optimal consumption is still (x1,X2) respectively. Hence here substitution effect is zero.
   Now to understand the income effect, we will consider the real income as variable. Thus as price of coffee rises, consumer's purchasing power or real income M/P falls where M= nominal income and P= price level. As the real income falls, consumer feels poorer and the budget line shifts leftward from DE to AC which becomes tangent to the new indifference curve IC2 at point E1. Thus the movement from point Eo to E1 along which the consumption of coffee falls from X1 to X3 and the consumption of donut decreases from X2 to X4 is due to the income effect only. Hence here total effect for a rise in the price of coffee is due to the income effect only and the substitution effect is zero.