Question

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 Andrew's preferences are given by: 1/2 1/2 Assume the price of Bikes is 1 and the price of computers is p. The initial endowments are BA = 10, Bs= 20, CA" 20 and Cs= 10, what is the equilibrium price of computers relative to bikes (p)? Answer:

pls answer this question in detail, thanks a lot

Answer 1

Determine the demand equations using the incomes and preferences.

Sarah's income is-

20+10p=YS

Her demand cuves are=

BS = YS/3 = (20 + 10p)/3

CS = 2YS/3p = (40 + 20p)/3

Andrew's income is-

10 + 20p = YA

His demand curves are:

BA = YA/2 = 5 + 10p

CA = YA/2p = (5 + 10p)/p

Setting supply ( BA + BS = 30 ) equal to demand, we have

30 = (20 + 10p)/3 + 5 + 10p

Solving the above equation, we have

p = 55/40 = 1.375

Equating the supply and demand for computers will yield the same result.