Question

1. (20 points) Let (x1, x2) be some interior bundle on the budget constraint, and suppose pi = 4 and P2 = 2. If the marginal rate of substitution at (x1, x2) is -3, then is (x1, x2) optimal? Explain why or why not, and justify your answer with economic intuition. (Partial credit for a purely graphical argument.)

Answer 1

Answer-1

Using the insights of consumer theory, the optimal bundle is one which satisfies the following equilibrium condition-

Slope Of Indifference Curve = Slope Of Budget Line

Marginal Rate Of Substitution (MRS_x1,x2) = Marginal Rate Of Exchange (MRE)

MU_x1 / MU_x2 = p₁ / p₂

Given ,

At (x1,x2), MRS =-3

p1 = 4 and p2 = 2

we have, p1/p2 = 4/2= 2

Since the slope of indifference curve (-3) is not equal to the slope of the budget line (2) , the bundle (x1,x2) is not optimal.

We have, | MRS |  > p1/p2 , which has the following economic intuition-

MRS tell us how much of good x2 a consumer willing to accept in return for one x1. Further, the price ratio tells us how much of good x2 the consumer will be able to buy by sacrificing one unit of x1. Now, since the marginal rate of substitution is greater than the price ratio, it implies that the consumer is willing to pay more for X1 than the price prevailing in the market (p1). In order to maximise his utility , the consumer should buy more of X1. By consuming more of X1, the utility derived from consumption of additional units of x1 will fall and hence the marginal utility of Good x1 will decrease .As a result, MRS falls till it becomes equal to the ratio of prices and the equilibrium is established at the point where the MRS equals the price ratio. At equilibrium the consumer’s utility is maximised and the corresponding bundle of Good is the optimal one.