Question

12) Answer the question on the basis of the following marginal utility data for products X & Y. Assume the prices of X and Y are $4 and $2, respectively, and that the consumers income is $18.

Units of x Marginal Utility, Y 16 14 12 Marginal Utility, x Units of Y 20 162 12 4 6 5 4 | 6 | 12 10 What quantities of X and Y should be purchased to maximize utility? Multiple Choice о 2 of X and 1 of Y о О 4 of x and 5 of Y 2 of X and 5 of Y оо 2 of X and 6 of Y

Answer 1

Solution:

The optimal quantity bundle of goods X and Y occurs where marginal utility per unit price for two goods is equal. In other words, MUx/Px = MUy/Py ; where MU is marginal utility and P is price of the respective goods.

So, we have MUx/MUy = Px/Py

MUx/MUy = 4/2 = 2 (or if not exactly equal, then in close proximity or approximation).

Further, the quantities should obviously lie in the budget of consumer, that is, it should also satisfy:

Px*X + Py*Y <= M ; where X and Y are quantities of 2 goods and M is income

4*X + 2*Y <= 18

From among the given options, in order to purchase (B) or (D), a higher income level is required. For (B), 4*4 + 2*5 = $26 is required. For (D), 4*2 + 2*6 = $20 is required. So, we eliminate these 2 options.

Choosing option (A) will generate a lower level of total utility.

Total utility = (20 + 16) + 16 = 52

Also, MUx/MUy = 16/16 = 1 < 2, so more of good Y shall be purchased (and we do have income left for that).

Finally, option (C) will have: MUx/MUy = 16/8 = 2, and generate a lot higher total utility level: (20 + 16) + (16 + 14 + 12 + 10 + 8) = 36 + 60 = 96

So, correct option is (C) 2 of X and 5 of Y.