Question

During the first week of lockdown, you decided not to spend more than $30 on your food. You ate only hotdog with burger bread, and that also in a 1:1 combination, and nothing else. The prices of both these goods were $1 per unit. Find out the optimum amount of hotdog and burger bread you consumed that week. In the second week, due to lack of supply the price of hotdog increased to $2 while the price of burger bread did not change. How many hotdogs and burgers bread did you consume in the second week? Explain the income and substitution effects of this price change using a diagram

Answer 1

In the first week of Lockdown:

Since the consumption of both the goods take place in 1: 1 ratio. The quantities of both the good remains same.

Also the price of both goods = $1

The budget constraint will be:

1H + 1B = 30

where H = no. of hot dogs and B = burger

since the consumption is in ratio 1: 1

1H + 1H = 30

2H = 30

H = 15

B= 15

The optimum quantity of Burger and hotdog he will consume in the first week given his budget = 15 units of burger and 15 units of hotdog

In the second week of lockdown:

The budget constraint will be :

2H + B = 30

Now we know that the consumer consumes both the goods in equal fixed proportion of 1:1, which makes hotdogs and burgers as complimentary goods. In case of complimentary goods, there is zero substitution effect and the entire price effect becomes equal to the income effect, which reults in decrease in qunatity demanded of both the goods, given the price increase in one of the good. The utility function for such goods will be:

U = min (H,B)

which means,

H = B

So, 2H + H = 30

3H = 30

H = 10

B= 10

Hence in the second week of lockdown, the optimum quantity of hotdogs and burgers consumed will be 10 units each.

The situation can be represented using the above graph. The x axis represents the quantity of Hotdogs and the y axis represents the quantity of burgers. Since both the goods are consumed in fixed proportions, the IC curves will be perpendicular in shape. Due to the price increase of hotdoges the budget line will shift inwards corresponding to the x axis which is visible as the budget line AB1 becomes AB2 and touches IC curve U2 which is at lower level than U1. At U2, the quantity demanded of both hotdogs and burgers will decline. In the above graph we see that when the consumer is compensated for the loss of the purchasing power arising due to increase in price of hotdogs, (AB3) it will keep the consumer's quantity preferences unchaged indicating the fact that the consumer will consume same quantity as he was consuming before the price increase. This represents zero subctitution effect and the entire price effect from a to b point will constitute the income effect of the price change.