Question

Please show the work

1. The following table shows the marginal benefit of activity X and Y. The price of X is $4 and the price of Y is $2.

Quantity	MBx		MBY
1	20		14
2	16		12
3	12		8
4	10		6
5	8		5
6	6		4

a. Calculate the marginal benefits per dollar for each activity and put the values in columns 3 and 5 of the above table.

2. If the total budget is $20, the optimal levels of activity X and Y are _____ and ____ units, respectively.

c. If the total budget is $26, the optimal levels of activity X and Y are ____ units and _____units, respectively.

Answer 1

a)

Quantity	MBx	Marginal Benefit per dollar of X	MBY	Marginal Benefit per dollar of Y
1	20	20/4=5	14	14/2=7
2	16	16/4=4	12	12/2=6
3	12	12/4=3	8	8/2=4
4	10	10/4=2.5	6	6/2=3
5	8	8/4=2	5	5/2=2.5
6	6	6/4=1.5	4	4/2=2

The good with higher marginal utility per dollar will be preferred first.

b) If the total budget is $20, the optimal levels of activity X and Y are 3 and 4 units, respectively.

c) If the total budget is $26, the optimal levels of activity X and Y are 4 and 5 units, respectively.

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