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.

The price changes you need to examine is assume that both prices fall with price of food falling by a higher percentage relative to clothing.

(a)

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

Solution:

a)

Since percentage fall in price of food is greater than in price of clothing ,relative price of food will fall ,

eg , let price of F be 100 and of C be 200 , reltive pricw of F is 100/200 = .5,

if price of F falls 20%, it becomes 80

if price of C falls 10% , it becomes 180 , rltive price of F is 80/180 =0 .44 .

b)

Clothing should be normal good as food is is already an inferior good . In a consumer's basket all goods can not be inferior . If all goods are inferior increase in income will reduce demand for all goods leaving some unspent income.

c)

Due to price change consumption of food falls and of clothing increases.Income effect of price change(assumed to be stronger than substitutuin effect) reduces consumption of food which is an inferior good and increases consumption of clothing which must be normal good.

d)

Under the conditions given it is possible that consuption of both goods increase after price change, this can happen only when food is a non Giffen inferior good . However, it is not posible to reduce consumption of clothing after given direction of price change.

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