Question

In a two goods (x and y) world, two districts (A and B) are identical, except the prices of good x (Px) and good y (Py) are higher and lower in district A, respectively. Suppose two identical individuals (i.e. same preferences and income) live in the two districts separately and their optimal choices are interior solutions.

Is the statement: “The MRS at the optimal choices of two individuals are the same” true, false, or uncertain? Explain your answer intuitively and graphically.

Answer 1

Let us first see the budget line of two consumers in different districts each:




As we can see:
(i) in District A the consumer can buy less quantity of good x because x is pricier here than in district B
(ii) in District A the consumer can buy more quantity of good y because y is cheap here than in district B

The two budget line slopes in two district is different from each other. Budget line District A has a steeper slope whereas budget line in District B has a moderate slope only.

Now, talking about the optimal point (or consumer equilibrium point), we know that in order to ascertain the optimal point the following condition has to satisfy:

MRS_xy = P_x / P_y

Here:
MRS_xy is the slope of IC curve; and
P_x / P_y is the slope of budget line.

Well now, as suggested in the question, two individuals are identical, which means both have same preferences and income. We can comfortably say that MRS_xy of both the individual consumers living in two different districts are same. In other words the slope of their Indifference curve are same and identical.

But as the diagram above suggests, their slope of budget line, as indicated by P_x / P_{y ,} is not the same.

Can you smell it? Actually, the optimal choices of two consumers can not be same. Even if MRS_xy is same, but P_x / P_y is not. How can two be the same when one of the deciding variable is different from the other. Therefore the statement given is false.