Question

1. (a) Outline the income and substitution effect of a price rise for an inferior good. Under what circumstances will the demand curve slope downwards for an inferior good. Illustrate using a diagram. (b) (c) Bob views apples and oranges as perfect substitutes in his consumption, and MRS 1 for all combinations of the two goods in his indifference map. Suppose the price of apples is $2 per pound, the price of oranges is $3 per pound, and Bob's budget is $30 per week. What is Bob's utility maximizing choice between these two goods? Illustrate your answer with a diagram.

Answer 1

1.

(a)

Before answering this question let us look at the definition of the inferior good :-

A good is called inferior if the quantity demanded of that good decreases with increase the income of the consumer.

In case of inferior goods the income and substitution effect works in opposite directions,and the combined result of a price change is indeterminate.

why?

Because a consumer will always buy less of a good if the price of that good increases hence, the substitution effect will always work in negative direction no matter good is inferior or normal. But the income effect will be positive in case of inferior goods (look at the definition) . When we increase the price of the good the consumer will feel poorer cause real income of the consumer will fall hence this will cause the quantity demanded of the inferior good to be increased hence, an increase in price will cause an increase in the quantity demanded of that good. So, both the income and substitution effect will work in opposite direction and net result will depend on the magnitude of both the effects.

(b)

This will happen when income effect will be dominated by the substitution effect,that is if the magnitude of substitution effect will be greater than the income effect then the increase in price of that good will result in fall in quantity demanded of that good and hence the demand curve will be downward sloping.

attaching the diagram below:

(c)

He will consume only apples, and no orange. Think about it intuitively why?

Hint: Both apple and orange are perfect substitutes and Px>Py i.e., price of orange is greater than price of apple. What would you do as a utility maximizing consumer?

I am attaching the numerical solution below however:

In the diagram above shifting the IC in upward direction will give higher utilities and we will keep shifting the IC until we reach at the optimal point, moving beyond that point is not possible due to budget constraint hence IC3 is the highest IC and hence will give the maximum utility that we can get.