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Perfect substitutes. MRS=a Given the prices and income P1, P2, and I, solve for the consumer’s...

Perfect substitutes. MRS=a Given the prices and income P1, P2, and I, solve for the consumer’s optimal choices?

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Answer #1

Ans. If the goods are perfect substitutes, the consumer will spend all his income on the good which is relatively cheaper and at equilibrium,

Marginal Rate of Substitution = Price of good 1 / Price of good 2

=> a = P1/P2

So, there are three cases for equilibrium,

i) a > P1/P2 (i.e. P1 < P2), consumer will consume only good 1 because it is cheaper, so,

demand function for good 1 is x1 = I/P1

and demand function for good 2, x2 = 0

ii) a < P1/P2 (i.e. P1 > P2), consumer will only consume good 2 because it is cheaper, so,

demand function for good 1, x1 = 0

and demand function for good 2, x2 = I/P2

iii) a = P1/P2 (i.e. P1 = P2), consumer will be indifferent between the two goods and can consume any quantity of x1 and x2 on the budget constraint.

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