Question

1. The table shows the total utility (TU) that James receives from consuming different amounts of two goods X and Y, per month.

Quantity	TUx	MUx	MUx/Px	TUy	MUy	MUy/Py
0	0			0
1	50			75
2	88			117
3	121			153
4	150			181
5	175			206
6	196			225
7	214			243
8	229			260
9	241			276

1. Fill in the other columns of the table by calculating the marginal utilities for goods X and Y and the ratios of marginal utilities to price for the two goods. Assume that the price of both goods X and Y is $3.

2. If James allocates $30 to spend on both goods, how many units will he buy of each?

3. How much will James spend on each good at the utility maximizing combination?

4. How much total utility will James experience by buying the utility-maximizing combination?

5. Suppose the price of good Y increases to $6. How many units of X and Y will he buy to maximize his utility now?

Answer 1

Quantity	TUx	MUx	MUx/Px	TUy	MUy	MUy/Py
0	0			0
1	50	50	16.67	75	75	25.00
2	88	38	12.67	117	42	14.00
3	121	33	11.00	153	36	12.00
4	150	29	9.67	181	28	9.33
5	175	25	8.33	206	25	8.33
6	196	21	7.00	225	19	6.33
7	214	18	6.00	243	18	6.00
8	229	15	5.00	260	17	5.67
9	241	12	4.00	276	16	5.33

James will buy those units which has highest MU dollar

he will buy 5 uints of both the products to maximise his utility by folllowing these rankings as shown in table

Quantity	MUx/Px	Rank	MUy/Py	Rank
1	16.67	2.00	25.00	1.00
2	12.67	4.00	14.00	3.00
3	11.00	6.00	12.00	5.00
4	9.67	7.00	9.33	8.00
5	8.33	9.00	8.33	10.00
6	7.00		6.33
7	6.00		6.00
8	5.00		5.67
9	4.00		5.33

3.) Spending on Utility Maximisation

X= 5*3 = 15

Y = 5*3 = 15

4)

Quantity	MUx/Px	MUy/Py
1	16.67	25.00
2	12.67	14.00
3	11.00	12.00
4	9.67	9.33
5	8.33	8.33
	58.33	68.67

TOTAL = 58.33+68.67 = 127

5.

Quantity	MUx/Px	Rank	MUy/Py	Rank
1	16.67	1	12.50	3
2	12.67	2	7.00	7
3	11.00	4	6.00
4	9.67	5	4.67
5	8.33	6	4.17
6	7.00	8	3.17
7	6.00		3.00
8	5.00		2.83
9	4.00		2.67

X = 6 Units

Y = 2 Units

TOTAL EXPENSE = 6*3 + 2*6 = $30