Sarah and Andrew Are Two Traders in a Pure Exchange

question 29

Essay

Sarah and Andrew are two traders in a pure exchange economic with two goods,Bikes (B)and Computers (C).Sarah's preferences are described by the Cobb-Douglas Utility function:
U_S = B_S^1/3C_S^2/3
Andrew's preferences are given by:
U_A = B_A^1/2C_A^1/2
Assume the price of Bikes is 1 and the price of computers is p.The initial endowments are B_A = 10,B_S = 20,C_A = 20 and C_S = 10.Solve for the competitive equilibrium prices (relative prices)and quantities.

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Definitions:

Wage

A wage is the compensation paid to employees for their labor, typically calculated on an hourly, daily, or piecework basis.

Output

The quantity of goods or services produced in a given period by an individual, firm, or country.

Marginal Revenue Product

The additional revenue generated from employing one more unit of a factor of production, holding all other factors constant.

Marginal Product

The additional output gained from employing an extra unit of input in the production process.