Question

Suppose a consumer has the utility function u(x,y)=x+y -

(a) In a well labelled diagram illustrate the indifference curve which yields a utility level of 1

(b) If the consumer has income And faces the prices Px and Py for x and y, respectively, derive the demand function for the two goods

(c) What types of preferences are associated with such a utility function?

Answer 1

U= X+Y

a)

1 = X+Y

If X=0 then Y=1

If Y=0 then X=1

b)

For demand function:

MRS= Marginal utility of good X(MUX) / Marginal utility of good Y(MUY)

Marginal utility of good X(MUX)= Differentiation of U wrt X= 1

Marginal utility of good Y(MUY)= Differentiation of U wrt Y= 1

MRS= 1, It implies that both can be use on place of one another with rate of subtitution =1.

So If Px < Py, Consumer will consume only good X:

X= Income/Px Demand function for Good X

So If Px > Py, Consumer will consume only good Y:

Y= Income/Py Demand function for Good Y

c)

This utility function implies that preferences are perfect substitutes that is goods are perfectly substitute with each other.