Question

Consider a consumer with a utility function U = x^2/3y^1/3, where x and y are the quantities of each of the two goods consumed. A consumer faces prices for x of $2 and y of $1, and is currently consuming 10 units of good X and 30 units of good Y with all available income. What can we say about this consumption bundle?

Group of answer choices

a.The consumption bundle is not optimal; the consumer could increase their utility by consuming more of good Y and less of good X.

b.The consumption bundle is not optimal; the consumer could increase their utility by consuming more of good X and less of good Y.

c.The consumption bundle is not optimal; given the prices, the consumer should consume only good Y and none of good X.

d.The consumption bundle is optimal; the consumer has reached their highest indifference curve given their budget constraint.

Answer 1

Correct Answer:

B

Working note:

U = x2/3y1/3

MUx = (2/3)*(Y/X)^(1/3)

MUy = (1/3)*(X/Y)^(2/3)

Further, for optimum level of consumption,

MUx/Price of X = MUy/ price of Y

(2/3)*(Y/X)^(1/3) / 2 = (1/3)*(X/Y)^(2/3)/1

(Y/X)^(1/3) = (X/Y)^(2/3)

Y = X

So, one unit of Y can be substituted by 1 unit of X. But, at the present time, 10 unit of X and 30 units of Y are being consumed. So, it is not an optimum bundle. consumption of X should be increased and consumption of Y should be decreased.