Question

3. When prices are (p1,P2) (1,2) a consumer demands (xi, 2) (1,2), and when prices are (p1,P2) (2,1) the consumer demands (x1,x2)-(2,1). Is this behavior consistent with the model of utility maximization?

Answer 1

3 Consider the given problem here the initial price is “(P1, P2) = (1, 2)” and the initial choice is “(X1, X2)=(1, 2)”. So, here the income of the consumer is the value spent on the choice bundle, => “M=1*1+2*2=5”.

Consider the following fig.

Now, consider the following fig, where “C1D1” be the initial budget line where “A(1,2)” be the choice. Now, let’s assume that when price is “(P1, P2) = (2, 1)” and the corresponding choice is “B(2, 1)”. So, here the income of the consumer is the value spent on the choice bundle, => “M=1*1+2*2=5”, and “C2D2” be the budget line corresponding to this situation. So, in both the cases we can see that the income is “5” and in the initial case “A” was chosen when “B” was also affordable (because "B" is inside of "C1D1), but in the 2nd case “B” is chosen when “A” is also affordable (because "A" is inside of "C2D2). So, this is not consistent with utility maximization. Since initially “A” was chosen when “B” was affordable, => there must not be any case where “B” will be chosen when “A” is affordable. If “B” is chosen then “A” must be unaffordable.