Question

Old: Aria consumes only potatoes and cheese. When the price of potatoes was $9 a sack and the price of cheese was $5 a packet, he spent his entire income to buy 5 sacks of potatoes and 10 packets of cheese per month.

New: Now, the government subsidizes potatoes. Market prices are the same, but consumers get $5 in subsidy for every sack of potatoes they buy. To pay for this subsidy, the government has introduced an income tax of $20 a month.

a. What is Aria’s new budget equation?

b. Can Aria afford more or less on potatoes and cheese than before?

Answer 1

Answer

(a)

Budget line is given by :

Price of Potatoes*Quantity of Potatoes + Price of Cheese*Quantity of Cheese = Income.

It is given that When the price of potatoes was $9 a sack and the price of cheese was $5 a packet, he spent his entire income to buy 5 sacks of potatoes and 10 packets of cheese per month

So her income = 9*5 + 5*10 = 95.

Hence Budget line is given by :

9P + 5C = 95 where P = number of sacks of potatoes , C = number of packets of cheese.

It is given that they will get $5 subsidy for every P they purchase. Thus now, Price of a sack of potato is 4 instead of 9 and her income will 95 - 20= 75 because government has introduced an income tax of $20 a month.

Hence Now we have the following budget equation:

(9 - 5)P + 5C = 95 - 20 (or you an say 9P + 5C = 95 + 5P - 20 => (9 - 5)P + 5C = 75)

=> 4P + 5C = 75 ----------------------Aria’s new budget equation

(b)

Previously she was buying 5 sacks of potatoes and 10 packets of cheese per month i.e. P = 5 and C = 10. Lets see that can she purchase that even now.

As discussed above now Price of potato = 4 and price of cheese = 5(same). Thus 4P + 5C = 4*5 + 5*10 = 70. Thus after buying previous quantities she still have $5 left from which she can buy more of potatoes and cheese. Thus, Now Aria can afford more potatoes and cheese than before.