Question

Eggplants and tomatoes are perfect complements for Mario, since the only recipes he knows use tomatoes(denoted as x) and Eggplants(denoted as y) together in a 1:2 ratio. One week his garden yielded 10 pounds of tomatoes and 40 pounds of eggplant. At that time the price of each vegetable was $5 per pound. a. What is the monetary value of Mario's endowment of vegetables. b. The price of tomatoes rose to $20, while the price of eggplant stayed at $5. Calculate the final optimal consumption bundle and the endowment income effect on Mario's tomato consumption after the price change. (Round to two decimal places)

Answer 1

a).

Here the price of tomatoes and eggplant are $5 per pound. The production of tomato is 10 pound and 40 pound. So, the monetary value of Mario’s endowment of vegetables is “$5*10 + $5*40 = $250”.

b).

Here Mario want to consume “E=eggplant” and “T=tomato” in fixed proportion “2:1”, => the utility function is “U = min(E/2, T/1)”, => at the optimum “E=2*T”.

The budget line is given by, => Pe*E + Pt*T = m1, where “m1=250” and “E=2*T”.

=> Pe*E + Pt*T = m1, => Pe*(2*T) + Pt*T = m1, => [2*Pe + Pt]*T = m1, => T = m1/[2*Pe + Pt] = 250/(2*5+5) = 16.67, => T = 16.67 pounds.

From the utility function we have, => E = 2*T, => E = 2*16.67 = 33.34, => E = 33.34 pounds.

Now, let’s assume the price of tomato increases to $20 from $5 but the price of eggplant remains the same at $5, => the value of the endowment increases to “m2 = Pe*E + Pt*T = $5*40 + $20*10 = $400 = m2”.

So, the optimum vegetable consumption are given by, => T = m2/[2*Pe + Pt] = 400/(2*5+20) = 13.33, => T = 13.33 pounds. From the utility function we have, => E = 2*T, => E = 2*13.33 = 26.66, => E = 26.66 pounds.

Here the utility function of Mario is perfect complement types, => the entire change is coming from the income effect of endowment. So, the income effect on Mario’s tomato consumption is “13.33 – 16.67 = (-3.34) pounds of tomato”.