Question

Take Jeremy’s total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremy’s utility.

Short answer

The best possible outcome is one round trip and 160 minutes of phone call minutes.

Step-by-step solution

Step 1. Introduction:

Marginal utility is the additional utility received through the consumption of one additional unit of commodity. Whereas, the marginal utility per dollar is the extra enjoyment attained from buying a commodity given the cost of the commodity denoted by MU / P.

Step 2. Marginal utility:

The first step is to compute marginal utility using the total utility statistics in the table beneath, recognizing that marginal utility equals the change in total utility divided by the change in trips or minutes.

Round Trips	Total utility	Marginal utility per trip	Phone Minutes	Total utility	Marginal utility per minute
0	0	-	200	1100	-
1	80	80	160	1040	60 / 40 = 1.5
2	150	70	120	900	140 / 40 = 3.5
3	210	60	80	680	220 / 40 = 5.5
4	260	50	40	380	300 / 40 = 7.5
5	300	40	0	0	380 / 40 = 9.5

Step 3. Marginal utility per dollar:

Marginal utilities cannot be compared because the units round trips and phone call minutes are being compared. For comparison there has to be a common denominator which is price. Dividing marginal utility by price gives column 4 and 8 in the table beneath:

Round trips	Total utility	Marginal utility per trip	MU / P	Phone Minutes	Total utility	Marginal utility per minute	MU / P
0	0	-	-	200	1100	60/40 = 1.5	1.5/0.05 = $30
1	80	80	80/2 = $40	160	1040	140/40 = 3.5	3.5/0.05 = $70
2	150	70	70/2 = $35	120	900	220/40 = 5.5	5.5/0.05 = $110
3	210	60	60/2 = $30	80	680	300/40 =7.5	7.5/0.05 = $150
4	260	50	50/2 = $25	40	380	380/40 = 9.5	9.5/0.05 = $190
5	300	40	40/2 = $20	0	0	-	-

Step 4. Explanation:

Begin at the bottom of the table, where the total number of round trips and phone minutes is calculated (5, 0). This is a random beginning place, however the numbers in this sample work much better if you start from the bottom. Let's say we want to go to the next level up. The marginal utility per dollar spent on a round journey is 25 at (4, 40). For every dollar spent on phone minutes, the marginal utility is 190. Since 25 190, we've gotten a lot more bang for our buck when it comes to phone minutes, so let's use them more. MU/PRT is 30 150 (the MU/PM) at (3, 80), but observe how the difference is narrowing. We continue to exchange round trips for phone minutes until we reach (1, 160), which is the best we can accomplish. The MU/P comparison is as accurate as it gets (40 vs. 70).