Question

Use the table below for total utility for both Good A and Good B and calculate and plot both the marginal utility and the total utility on the same graph with the utility on the vertical axis and quantity on the horizontal axis. Assume the price of Good A is $2 and the price of Good B is $1 with an income of $12. Using the utility-maximizing rule that the marginal utility per dollar for each good must be equal, identify the bundle of goods that will maximize this person's utility given that all her income is spent.

Quantity	Total Utility for Good A	Total Utility for Good B	Marginal Utility of Good A (MUa)	Marginal Utility of Good B (MUb)
0	0	0
1	16	11
2	30	21
3	42	30
4	52	38
5	60	45
6	66	51
7	70	56
8	72	60

Answer 1

Quantity	Total Utility for Good A	Total Utility for Good B	Marginal Utility for Good A	Marginal Utility for Good B	MUA / PA	MUB / PB
0	0	0	--	--	--	--
1	16	11	16	11	8	11
2	30	21	14	10	7	10
3	42	30	12	9	6	9
4	52	38	10	8	5	8
5	60	45	8	7	4	7
6	66	51	6	6	3	6
7	70	56	4	5	2	5
8	72	60	2	4	1	4

Price of Good A = $2

Price of Good B = $1

Income =$12

So the budget equation will be

2A + 1B = 12

Now for utility maximization, we have to attain this situation

and also see whether the bundle is fulfilling the budget equation

So from the above table, there are five places where

1) 1 unit of good A and 4 units of good B

2) 2 units of good A and 5 units of good B

3) 3 units of good A and 6 units of good B

4) 4 units of good A and 7 units of good B

5) 5 units of good A and 8 units of good B

Now we have to check whether these five bundles are fulfilling the budget equation

1) 1 unit of good A and 4 units of good B

2A + 1B = 12

2(1) + 1(4) = 12

2 + 4 = 12

6 is not to 12

Hence this bundle will be rejected as it is not fulfilling the budget equation

2) 2 units of good A and 5 units of good B

2A + 1B = 12

2(2) + 1(5) = 12

4 + 5 = 12

9 is not to 12

Hence this bundle will be rejected as it is not fulfilling the budget equation

3) 3 units of good A and 6 units of good B

2A + 1B = 12

2(3) + 1(6) = 12

6 + 6 = 12

12 = 12

4) 4 units of good A and 7 units of good B

2A + 1B = 12

2(4) + 1(7) = 12

8 + 7 = 12

15 is not to 12

Hence this bundle will be rejected as it is not fulfilling the budget equation

5) 5 units of good A and 8 units of good B

2A + 1B = 12

2(5) + 1(8) = 12

10 + 8 = 12

18 is not to 12

Hence this bundle will be rejected as it is not fulfilling the budget equation

Hence 3 units of good A and 6 units of good B will give a person maximum satisfaction