Question

10. The figure shows two indifference curves and two budget constraints for a consumer named Kevin.

Number of Sweaters B 28 21 0 12 35 63 Number of Shirts (a) If Kevin's income is $1,260, then what is the price of a sweater? (b) Suppose point A was Kevin's optimum last week, and point B is his optimum this week. What happened between last week and this week? (c) If point A is Kevin's optimum, then at that optimum, what is his opportunity cost of a shirt in terms of sweaters? (d) Suppose Kevin is optimally purchasing 21 shirts and 28 sweaters, and he is spending $1134 on shirts. What is the price of a sweater? (e) For Kevin, are sweaters and shirts substitutes, complements, or neither?

Answer 1

(a) The price of sweater = 30 dollars if Kevin has 1260 dollars.

Solution- We see that wehen 0 shirts are demanded , quantity of sweaters is 42.

We also know budget = 1260 dollars

Therefore budget = Price of sweater * Quantity of sweater + price of shirt * quantity of shirt

1260   = Price of sweater*42 + 0* quantity of shirt

Price of sweater = 1260/42=30 dollars

(b) From A to B Kevin moves to a higher indifference curve and hence his overall utility is maximised. This is because his budget has increases and he can afford more of both the commodities. However in this given scenario Kevin opts to buy 9 (i,e, 21-12) shirts more from the extra income.

(c) Opportunity cost is the cost of the foregone alternative. Here we look at the budget constraint for A and opportunity cost will be ratio of the slope of the budget constraint = (42-28)/(12-0)=14/12 = 1.167

Thus opportunity cost is for increase in 1 shirt, 1.167 sweaters have to be sacrificed.

(d) Price of sweater = 81 dollars

Solution:-

Here we know price of a shirt = Money spent on shirt/ number of shrits=1134/21= 54 dollars

Now total budget = 54*number of shirts bought when no sweaters are bought

= 54*63

= 3402

Now price of sweater = 3402/ number of sweaters bought when shirts bought is zero

= 3402/42

= 81 dollars

(e) For Kevin sweaters and shirts are neither substitute or complements. Kevin shows normal preferences which mean that consumer would want to trade some part of each good to continue consumption of both simultaneously.

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