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In a two goods (x and y) world, two districts (A and B) are identical, except...

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. Evaluate the following statement: ‘The MRS at the optimal choices of two individuals are the same’. True, false, or uncertain? Explain your answer intuitively and graphically. (draw indifference curves and budget constraints)

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Answer #1

Sol;

Let us asume following

PXA = 4 , PYA = 2 , PXB = 2 , PYB = 4, IA = IB = 100

Budget constraint of A is

4X + 2Y = 100

slope of budget line = 4/2 = 2

Budget constraint of B is

2X + 4Y = 100

slope of budget line = 2/4 = 1/2

Since slopes of the budget constraints of the two individuals are different , MRS at optimal choice will not be same.

It is because at optimal choice MRS equals slope of budget constraint.

Under our assumptions AB is budget line of A and CD is budget line of B . Assumede preference for both is

U = XY

EA is equilibrium point of A and EB is equilibrium point for B.

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