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 will depend on the 7th digit in your Student ID number as described by the alternative scenarios below. (My Student ID is 217225221, Thus, seventh number is 2 which is even)

• Scenario A: If the 7th digit in your Student ID number is odd (that is, it is either 1, 3, 5, 7 or 9), then assume that both prices fall with price of food falling by a higher percentage relative to clothing.

• Scenario B: If the 7th digit in your Student ID number is even (that is, it is either 0, 2, 4, 6 or 8), then assume that both prices go up with price of food increasing by a higher percentage relative to clothing.

(a) What is the 7th digit in your Student ID number? Based on this, which of the above two scenarios 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

(a) 7th digit in my student ID is 2 which is even. Scenario B applies to my case as my seventh digit is 2. I am required to examine that the price of both go up with price of food increasing with a high percentage relative to clothing.

(b) Clothing should be treated as a normal good as price of both goods are increasing but price of clothes are increasing less in relative to food. as we have considered the food as a inferior good so we should consider clothing as a normal good.

(c)

(d) As there is a reduction in food quantity as the price is increasing and there is increase in clothing as relative price rise is less than clothing. so direction of graph will be upwards only. yes there can be in opposite diectin also if we give food a normal good rather than inferior good .