Question

Farmer Frank lives on 100 acres on a rural farm where he raises chickens (which produce eggs) and grows tomatoes. Eggs and tomatoes are the only two goods that Frank consumes. This year, Frank's chickens will yield 100 eggs and 10 pounds of tomatoes, respectively.

(a) If Frank were not able to trade his endowment of tomatoes and eggs, but he can freely dispose of goods, what would his set of feasible consumption bundles look like? Show it on a graph.

(b) Suppose Frank could go to the Coventry Farmers' Market and buy or sell eggs for $0.10 each, while tomatoes could be bought or sold for $1.50 a pound. If Frank used all of his resources to buy tomatoes, how many pounds of tomatoes could he consume? If he used all of his resources to buy eggs, how many eggs could he eat? Draw Frank's new set of feasible consumption bundles.

(c) Suppose Frank's next door neighbor, Farmer Fran, who also raises chickens, gives Frank a gift of 50 eggs for Christmas. Frank would not consider selling Frank's gift at the Farmer's market; to do so would be rude. What does Frank's feasible set of consumption bundles look like after receiving this gift?

Answer 1

a) Frank can consume 100 eggs or 10 pounds of tomatoes or any less as he wishes. The consumption bundle is the area inside the rectangle under y=100 and x=10

b) Now Frank can sell his 10 pounds of tomatoes for 15$ and buy 150 eggs to have a total of 250 eggs or he can also sell 100 eggs for 10$ and get 6.67 pounds of tomatoes and have 16.67 or anything in between. The consumption bundle is the area inside triangle limited by the line y=250-15x(Can have a max of 250 tomatoes and your number of eggs reduce by 15 for every increase in pound of tomato,since a pound of tomato is 1.5$ and an egg is 0.1$)

c) Now Frank got 50 eggs as a gift but cannot sell the gifted 50 eggs but he can still sell his remaining 100 eggs and get 6.67 pounds of tomatoes. So he can have a maximum of 250+50 eggs=300 eggs and 0 pounds of tomatoes and he can trade 250 eggs to get uptil 16.67 pounds of tomatoes but no more than that,so he cannot go to the right of (16.67,50) and is thus limited by the line x=16.67. So his consumption bundle is trapezium under the line y=300-15x and to the left of x=16.67

Hope its clear. Do ask for any clarifications if required