Consider a consumer with textbook preferences defined over two goods X1 and Y2. Why is the...

Consider a consumer with textbook preferences defined over two goods X₁ and Y₂. Why is the condition MRS = p1/p2 necessary for utility maximization? Is this condition alone also sufficient?

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Expert Solution

Given Condition, MRS = P1/P2. Here, P1 is the price of X1 and P2 is the price of Y2.

Consumer always equilibrium when MRS = P1/P2 or price ratio. If this condition is not followed, then there are two conditions, the First condition is MRSxy > P1/P2 and seond condition is MRSxy < P1/P2.

If MRSxy > P1/P2, it means that the consumer is willing to pay more for X1 than the price prevaling in the market. As a resut, the consumer buys more of X1. As a result, MRS falls till it become equal to ration of prices and the equilibrium is established.

If MRSxy < P1/P2, it means that the consumer is willing to pay less for X than the price prevailing in the market. It induces the consumer to buy less of X1, and More of Y2. As a result, MRS rises till it becomes equal of the ration of prices and the equlibrium is established.

Yes, This condition is sufficient because MRS is the slope of indifference curve must be equal to the price ratio(the slope of budget line). So when MRS = price ratio the consumer could reach a higher indifference curve within the same budget set by altering the chosen bundle and higher indifference curve show higher level of satisfaction.

Rahul Sunny answered 2 months ago

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