Question

Mario consumes eggplants and tomatoes in the ratio of 1 bushel of eggplants per 1 bushel of tomatoes. His garden yields 30 bushels of eggplants and 10 bushels of tomatoes. He initially faced prices of $25 per bushel for each vegetable, but the price of eggplants rose to $100 per bushel, while the price of tomatoes stayed unchanged. After the price change, he would

a. increase his eggplant consumption by 6 bushels.

b. decrease his eggplant consumption by at least 6 bushels.

c. increase his consumption of eggplants by 8 bushels.

d. decrease his consumption of eggplants by 8 bushels. e. decrease his tomato consumption by at least 1 bushel.

Please show your work

Answer 1

The correct answer is (a) increase his eggplant consumption by 6 bushels.

Mario consumes eggplants and tomatoes in the ratio of 1 bushel of eggplants per 1 bushel of tomatoes. This means that he considers eggplant and tomatoes as perfect complements and hence is a leontief consumption function. Thus Utility is given by:

U = min{E,T}

Note that Utility for such function maximizes when consumer consumes at a kink point of an indifference curve(IC). Kink point of his IC occurs at E = T.

Initially he has 30 bushels of egg plant and 10 bushels of tomatoes. It is given that Price of bushels of tomatoes = price of bushels of eggplant = 25. As both have same per unit cost and hence can exchange 1 eggplant for 1 tomato. As he is having 30 bushels of egg plant and 10 bushels of tomatoes. Thus he will buy 10 tomatoes and sell 10 eggplant. Thus he swill end up consuming 20 bushels of tomatoes and 20 bushels of eggplant.

Now after the price changes It is given that Price of bushels of tomatoes = 25, price of bushels of eggplant = 100. Now his income = 100*30 + 25*10 = 3250.

Budget line is given by:

Price of eggplant*Quantity of eggplant + Price of tomato*Quantity of tomato = Income = 3250

100E + 25T = 3250. Also Kink will occur at E = T

=> 125E = 3250

=> E = 26

=> E = T = 26

Thus his consumption of Eggs after Price change is 26.

So, Change in consumption of Eggplant = 26 - 20 = 6 bushels of eggplant. Thu his consumption eff bith bushels of eggplant and bushels of tomatoes increases by 6 bushels.

Hence, the correct answer is (a) increase his eggplant consumption by 6 bushels.