Question

A consumer allocates all of her income between two goods, food and clothing, with the quantity of food consumed captured by the variable F while that of clothing by the variable C. The consumer has usual strictly convex preferences between the two goods. Assume that food is an inferior good and it is kept on the horizontal axis.

Suppose that the consumer’s income remains unchanged but prices of both of these goods change.

scenario: assume that both prices go up with price of food increasing by a higher percentage relative to clothing.

a, Based on this, which scenario apply to you? State the impact of the price changes you are required to examine on the relative price of food.

b. Determine whether clothing should be treated as a normal or inferior good and explain your answer.

c. Now proceed with doing a geometric analysis to portray one case that is logically consistent with the price change scenario you need to examine as specified in (a). In doing so, illustrate and explain how the consumer’s optimal bundle might change in response to the cumulative impact of these price changes.

d. Comment on whether the direction of total change in optimal quantities of food and clothing that you have shown in your diagram for part (c) are the only logically consistent possibilities. Or, is it also possible that changes could also be in the opposite direction? Explain your answer. You do not need to do additional diagrammatic analysis to answer this part.

Answer 1

Given that the allocation is between two goods :

Food (F) and Clothing (C)

==》Consumer has a strictly convex preference for both the goods - which means he prefers a weighted average of both the goods rather than more of a single good.

F is an inferior good for which the income effect is negative but the substitution effect is positive and relatively higher than the negative income effect. Therefore, the whole price effect becomes positive.

PE = IE + SE

Scenario : Prices of both F and C rises with a higher percentage rise for F than that of C.

A) Now, we know that there is a price rise for both the goods. The real income for the consumer declines. Therefore, a new budget constraint will be obtained with a higher decline in the budget at the horizontal axis which is indicated by a left ward shift in the budget constraint. Therefore, with the given information, demand for both good declines.

However, the decline in demand will not be proportionate to the change in price for the inferior good F due to the negative income effect. Therefore, the reduction in demand will be less than proportional to the hike in price.

Furthermore, the decline in demand for C is seen as proportionate to its price rise when we consider the less than proportionate change in F explained above. Hence, the new point of consumption will be diagonally below the previous point of consumption given the nature of reduction in demand for good 'F'.

B) Clothing here is inferred as a normal good as per the analysis. Because, the decline in demand will be proportionate to the rise in price due to the inferior nature of the good F and the resulting point of consumption.