Economics Problem set 6

6.2a
The objective of this problem is to found the price charged by Peter.

Firstly, the below table illustrate all P, TR, TC, MR and MC when there is different
Number of member served (Q).

No. of member served (Q)
Price per member(P)
Total revenue (TR)
Total cost (TC)
Profit
Marginal revenue (MR)
Marginal cost (MC)
1
400
400
190
210
400
190
2
380
760
380
380
360
190
3
360
1080
570
510
320
190
4
340
1360
760
600
280
190
5
320
1600
950
650
240
190
6
300
1800
1140
660
200
190
7
280
1960
1330
630
160
190
8
260
2080
1520
560
120
190
9
240
2160
1710
450
80
190
10
220
2200
1900
300
40
190

Profit will be maximized when marginal revenue is equal to marginal cost.
The given information cannot achieve the outcome of marginal revenue is equal to the marginal cost. However, the profit still can be maximized when marginal revenue is larger to marginal cost while these two quantities are very close to each other.
As a result, the profit is maximized when Peter serves 6 members and the price charged by him is $300.

6.2b
It is asked whether the profit can be increased if peter set two different prices to two groups which are adults and children group. If yes, what are the prices?

The profit will increase since group of customers has a different willingness to pay. Peter can set an optimum price to each group which is the prize they expected. Then the profit will rise.
The price for adult will remain at $300 with same explanation to 6.2(a).
The table below shows the situation on children group. Marginal revenue is larger to marginal cost while these two quantities are very close to each other when the charge is $240 so the price for children is $240.

No. of member served (Q)
Price per child
(P)
Total revenue (TR)
Total cost (TC)
Profit (TR-TC)

Marginal revenue (MR)
Marginal cost (MC)
1
280
280
190
90
280
190
2
260
520
380
140