Question

Jane’s utility function is U(x, y) = x + 2y, where x is her consumption of good X and y is her consumption of good Y. Her income is $2. The price of Y is $2. The cost per unit of X depends on how many units she buys. The total cost of x units of X is the square root of x.

1. The bundle ( 1 4, 3 4 ) is Jane’ s utility maximizing choice, given her budget.

2. The bundle (1, 1 2 ) is Jane’ s utility maximizing choice, given her budget.

3. Given her budget, Jane would maximize her utility by spending all of her income on

   good X.

4. Given her budget, Jane would maximize her utility by spending all of her income on

   good Y.

5. None of the above.

Answer 1

Answer: Option D is correct.

Given her budget, Jane would maximize her utility by spending all of her income on good Y.

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From the given utility function U(x, y) = x+2y, we can find the Marginal utility of both goods.

MUx = 1

MUy = 2

Her income is (m) = $2, and Price of Good y (P_y) = $2 and total cost of good x TC=

=> P_x * x = TC=

=> P_x  =

hence the budget equation :

m = P_x * x + P_y *y

=> 2 = P_x * x + 2 * y

Profit maximization formula can give us the value for  P_x = 1

with the given budget her utility will be maximized at bundle (1, 0.5)

U(1 , 0.5) = 2

Option A and B are incorrect as she can't afford to buy the bundle quantities mentioned in the option.

SInce MUy is higher than MUx, so she would choose to buy good Y over Good X, Purchasing 1 unit of Y she will maximize her utility Which is = 2.

Hence Option C and E are also incorrect.