Question

1. Suppose a consumer is maximizing utility consuming a bundle apples and bananas x and has standard preferences. Her budget constraint is given by the equation 1000-2a-2b0. Apples are normal goods and bananas are normal. a) plot the optimal bundle, showing the proper indifference curve and budget constraint. Call this bundle x1 b) show the effect of an increase of a single price increase for apples on the budget constraint. Use a hypothetical budget line to identify substitution effects for each good. Assume both goods are normal and indicate the appropriate income effect

Answer 1

1. Suppose the initial budget line is AB which is tangent to the initial indifference curve IC1 at point M with respect to which the optimal initial bundle is x1 and the initial quantity of apple is Q1 and initial quantity of banana is Q2 . Now suppose the price of apple has increased and the budget line will rotate inward from AB to AC which becomes tangent to a new indifference curve IC2 at point O with respect to which the optimal bundle is X3 I.e the quantity of apple is Q3 and quantity of banana is Q4. Now the total effect of this price increase can be decomposed into a substitution effect and an income effect.

Now to understand the substitution effect we will hold consumer’s real income constant. Hence consumer will stay on the initial indifference curve. But as the price ratio has changed due to an increase in the price of apples, consumers will stay on the budget line with it’s slope equal to the slope of the new budget line AC. 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 quantity of apples demanded decline from Q1 to Q5 and the quantity of bananas increases from Q2 to Q6 is due to the substitution effect because as the price of apples have increased, consumers substitute apples with bananas.

Now, to understand the income effect, we will consider real income as variable, Hence as the price of apples have increased, consumers real income M/P falls, and consumers will feel poorer hence the budget line shift leftward from DE to AC and the new budget line becomes tangent to the new indifference curve IC2 along which the quantity of apples decline from Q5 to Q3 and quantity of bananas decline from Q6 to Q4. Hence the movement from point O to point N is the income effect associated with an increase in the price of apples.

bundnar 9 A - ICI Qs me Qir B Apple substitution effect Income effect Scanned with CamScanner