Question

2. Following a freak peddle-boating accident, Sohail and Jimmy end up marooned on a deserted island. Although they are unable to produce anything, they are very fortunate and had packed cookies (?) and protein bars (?) in their fanny packs before heading out on their excursion.

Sohail has 6 cookies and 3 protein bars, while Jimmy has 3 cookies and 6 protein bars. Although they like the same products, they have different preferences over them;

Sohail’s utility function is ?(?, ?) = ??²

and Jimmy’s utility function is ?(?, ?) = ?²? .

The two castaways decide to engage in trade.

a. [8] Without normalizing prices, find their demand functions for each good.

b. [2] Write the excess demand function for cookies.

c. [6] Normalizing the price of protein bars, find the equilibrium price of cookies (?_?∗ ) that clears the two markets. How many cookies and protein bars does each of them consume in the competitive equilibrium?

d. [4] Are they each better off after engaging in trade than they would have been consuming their endowments? Show your calculations.

Answer 1

D) at initial Endowments

Us = 6*3*3 = 54, Uj = 3*3*6 = 54

At CE Allocations

Us' = 3*6*6 = 108

Uj' = 6*6*3 = 108

so both are better off