Question

Consider a local department store which only sells jeans (J) and sweaters (S). Jeans cost $30and sweaters cost $15. For each of the examples below, graph the budget constraint our consumer faces, putting J on the horizontal axis and S on the vertical one. Be sure to label our consumer’s initial bundle(what he comes into the store with).

a) The consumer comes into the store with 20 sweaters to exchange (and a gift receipt!).

b) The consumer comes into the store with 20 sweaters to exchange (and a gift receipt!). There is a 50% restocking fee.

c)The consumer comes into the store with 10 jeans and 10 sweaters to exchange (and a gift receipt!). There is a 50% restocking fee on jeans only.

Answer 1

Answer: Price of Jeans P_J = $30

Price of Sweater P_S = $15

The budget line formula:

M = P_J * J + P_S * S

M = 30J + 15S -----------------------------------------------(1)

J and S are quantities of Jeans and Sweaters respectively;  M= the total budget.

A). The consumer comes into the store with 20 sweaters to exchange (and a gift receipt!)

Since its a gift receipt, with this maximum 1 jeans or 1 sweater can be purchased. Since the price of jeans is higher, The gift receipt can be used to purchase 1 Jeans.

The total amount which she can get with the exchange = 20*15

=> M = 300 + (The gift receipt )

From equation 1

300 = 30J + 15S

=> S = 20 - 2J

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B).  The consumer comes into the store with 20 sweaters to exchange (and a gift receipt!). There is a 50% restocking fee

M = 300 - 150 + a gift receipt

=> M = 150 + a gift receipt

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C). The consumer comes into the store with 10 jeans and 10 sweaters to exchange (and a gift receipt!). There is a 50% restocking fee on jeans only.

M = 30 * 10 + 15 * 10 + A gift voucher - (30 *10 *50/100)

M = 300 + 150 - 150 + A gift Voucher

=> M = 300 + A gift Voucher

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