Question

Take Jeremy’s total utility information in question #1, and use it to calculate marginal utilities. Now, using only the information from the marginal utilities, start at the upper left-hand corner of the table given in problem (1) and explain why the optimal choice is the same as it was in the previous problem. Calculate the marginal utilities and verify the rule that at the optimal choice, P1 /P2 = MU1 / MU2. (Or in this case, that it is as close to equal as possible.)

Question #1 was Jeremy is deeply in like with Jasmine. He can either call her on the phone for 5 cents per minute or he can drive to see her, at a round-trip cost of $2 in gasoline money. He has a total of $10 per week to spend on staying in touch. To make his preferred choice, Jeremy uses a handy utilimometer that measures his total utility from personal visits and from phone minutes. Figure out the points on Jeremy’s budget set (it may be helpful to do a sketch) and identify his utility-maximizing point.

Round Trips	Total Utility	Phone Minutes	Total Utility
0	0	0	0
1	80	20	200
2	150	40	380
3	210	60	540
4	260	80	680
5	300	100	800
6	330	120	900
		140	980
		160	1,040
		180	1,080

Answer 1

The budget constraint of jeremy is:

where R is the number of rounds

P si the minutes of phone calls

Pr is the price of paid per round

Pp is the price paid per minute phone call

Jeremy maximises his utility when the marginal utility per dollar spend on phone call is equal to the marginal utility per dollar spend on rounds. which is subjected to his budget constraint.

Therefore.

We will find the marginal utility per round.

That is marginal utility per round = Change in total utility/ Change in rounds

Then marginal utility per dollar is the marginal utility divided by the price of a round trip. That is P_r = $2

We will find the marginal utility per minute of phone call.

That is marginal utility per minute= Change in total utility/ Change in minutes

Then marginal utility per dollar is the marginal utility divided by the price of a per minutes of phone call.

That is P_p = $0.05

Therefore,

When he takes the first round and takes 20 minutes phone call then his marginal utility per dollar spend on phone call is more than that of rounds.

That is,

therefore he will increase his minutes of phone call. As he is deriving more utility from the phone calls.

So he would take more phone calls. He will keep increasing the minutes of phone calls until the marginal utility derived from phone equals the marginal utility from rounds.

As we can see from the above tables that the marginal utility per dollar spend on phone is equal to the marginal utility per dollar spend on rounds are equal at : 1 round and 180 minutes of phone call.

But since he also has to keep his activity under budget of $10.

Now putting this quantity into the budget constraint to see if it satisfies his budget.

At consumption bundle (1 round and 180 minutes0.

The cost of the bundle is more than the budget. Therefore it is not the optimum bundle.

Therefore he will stop at 160 minutes. Which is the best optimal combination under his budget and according to the marginal utilities and price of the two activities. Therefore he will take 1 round and stop at 160 minutes of phone call. His closes utility maximization point is (1 round, 160 minutes of phone call) This point lies below the budget constraint as well as the indifference curve.

The indifference doesn't meet the budget constraint at any point. Therefore the optimum combination is not exactly equal to the marginal utility of per dollar of both the goods. But we get as close as we could.

Jerery's budget constraint:

The budget constraint is drawn by using the budget constraint equation. Where the rounds are shown on the x axis and minute of phone call on the y axis

The x intercept is the maximum rounds that jeremy could take with his budget of $10 when he only takes rounds and no phone calls.

That is putting

Similarly, minutes of phone calls when he take zero rounds.

Therefore the x-intercept is (5,0) and y-intercept is (0,200)

Jeremy's budget constraint:

Jeremy's utility maximisation point:

Now as we know that marginal utility per dollar is equal at (1 round,180 minutes) where the budget constraint is not satisfied.

Therefore the indifference doesn't cuts the budget constraint at any point. And after (1,180), the marginal utility per dollar spend on phone calls is more than marginal utility per dollar spend on rounds.

That is,

It means that the slope of the indifference curve is more than the slope of budget constraint. Therefore it is higher than the budget constraints.

BL is the budget constraint and IC is the indffierecne curve. They don't meet at any point and the IC is closest to the budget lien at (1,180) and after wards the distance keeps growing between indifference curve and budget constraint.

The closed optimal bundle is (1 round, 160 minutes phone call)