Suppose a consumer's level of satisfaction is given by AB² and he/she has a total of $10 to spend on goods A and B. If the price of A is $1 and the price of B is $2, and assuming you can only purchase whole units (not fractional) of A and B, how many units of A and B should he/she purchase? A) 2 units of A and 4 units of B. B) 4 units of A and 3 units of B. C) 6 units of A and 2 units of B. D) 0 units of A and 5 units of B.

Question

Quizplus · Accepted Answer

To maximize the consumer's satisfaction, we need to allocate the budget between goods A and B in such a way that the marginal utility per dollar spent on each good is equal.

The marginal utility of A is given by the first derivative of the utility function with respect to A, which is ABS1U1P1. Plugging in the prices, we get ABS1U11 = 1.

Similarly, the marginal utility of B is ABS1U2P2S1P0, which evaluates to ABS1U21 = 0.5.

Therefore, the consumer should allocate the budget in a way that he/she gets the same marginal utility per dollar spent on each good. Since the marginal utility per dollar spent on A is higher than that of B, it makes sense to purchase more units of A than B.

Using the budget constraint, we can set up the following optimization problem:

Maximize ABS1U1P12S1S1P0 
Subject to: P1A + P2B = 10

Plugging in the prices, the problem becomes:

Maximize ABS1U11A2S1S1P0 
Subject to: A + 2B = 10

Using trial and error, we can find that the optimal allocation is 4 units of A and 3 units of B, which gives a total utility of ABS1U14S1S1P0 = 26.

Suppose a Consumer's Level of Satisfaction Is Given by AB2

Suppose a Consumer's Level of Satisfaction Is Given by AB²