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. 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.

Answer 1

Above diagrams indicates the budget line of the consumers in the two districts.

It is given that the price of good x is higher and the price of good y is lower in district which means that the consumers in district A are buying more quantity of good y and less quantity of good x.

Hence, the slope of the budget line of district A is steeper whereas the slope of the budget line of district B is moderate.

The optimal condition refers to a point where the marginal rate of substitution between the two goods is equal to the price ratio of the two goods. This is represented as follows:

The slope of the budget line in the two districts are different. We know that the MRS is the slope of the indifference curve and the price ratio is the slope of the budget line.

It is also given that

(i) Two identical individuals

(ii) Have same preferences

(iii) Have same level of income

(iv) Different prices of the two goods

This means that the marginal rate of substitution of the two goods is different for both the individuals living in the different districts.  

Also, the slope of the budget line of the individuals in the two districts is not identical.

Hence, the statement is false.