Question

A consumer has utility function: u(x1 , x2 ) = x1 + 2x2 . The consumer has income m > 0 tospendongood1andgood2. Ifthepriceofx1 isp1 =1andthepriceofx2 isp2 =0.5, then, in order to maximize her utility, the consumer must consume:

a) x1 = x2 (b) x1 = 2x2 (c) 2x1 = x2 (d) x1 = 4x2

(e) None of the above

Answer 1

U(x₁, x₂) = x₁ + 2x₂   (Represents the utility function for perfect substitutes),

MRS = MU₁/MU₂

MU₁ =1

MU₂ =2

MRS =1/2 (slope of indifference curve)

P₁ =1 and P₂ =0.5

P₁/ P₂ = 1/0.5 (Slope of budget line)

Now, we can see that MRS< P₁/ P₂ .

Slope of the budget constraint is steeper than the slope of the indifference curve . This implies that to maximise the utility consumer must consume only good x₂. Because marginal utility per dollar for good x₁ i.e 1/1 =1 is less than marginal utility per dollar for good x₂ i.e 2/0.5 =4 . Hence, consumer spend all of his money income on good x₂ only.

Hence, option(E) is correct i.e none of the given options.