Suppose a firm is considering two different activities, X and Y, which yield the
ID: 1225707 • Letter: S
Question
Suppose a firm is considering two different activities, X and Y, which yield the total benefits presented in the schedule below. The price of X is $40 per unit, and the price of Y is $50 per unit.
Level of
activity
Total benefit of activity X
(TBX)
Total benefit of activity Y
(TBY)
0
$ 0
$ 0
1
1,200
1,300
2
2,160
2,550
3
3,040
3,750
4
3,840
4,750
5
4,560
5,650
a. The firm places a budget constraint of $360 on expenditures on activities X and Y. What are the levels of X and Y that maximize total benefit subject to the budget constraint?
b. What is the total benefit associated with the optimal levels of X and Y in part a?
c. Now let the budget constraint decrease to $230. What are the optimal levels of X and Y now? What is the total benefit when the budget constraint is $230?
Level of
activity
Total benefit of activity X
(TBX)
Total benefit of activity Y
(TBY)
0
$ 0
$ 0
1
1,200
1,300
2
2,160
2,550
3
3,040
3,750
4
3,840
4,750
5
4,560
5,650
Explanation / Answer
(a)
Level of activity
The price of X is $40 and the price of Y is $50. The equilibrium condition is:
MBx / Px = MBy / Py
The budget constraint is as follows: 40X + 50Y =360
Thus, the equilibrium level of activity is 4 units of X and 4 units of Y. It satisfies both the conditions stated above
MBx / Px = MBy / Py
MBx for 4 unit = $800, MBy for 4 unit = $1000
800 / 40 = 1000 / 50
And the budget constraint as follows:
40X+50Y = 360
40(4) + 50(4) = 360
(b) The total benefit associated with 4 units of X and 4 unit of Y is = 3840 + 4750 = $8590
(c)
The price of X is $40 and the price of Y is $50. The equilibrium condition is:
MBx / Px = MBy / Py
The budget constraint is as follows: 40X + 50Y =230
Thus, the equilibrium level of activity is 2 units of X and 3 units of Y. It satisfies both the conditions stated above
MBx / Px = MBy / Py
MBx for 2 unit = $960, MBy for 3 unit = $1200
960 / 40 = 1200 / 50
And the budget constraint as follows:
40X+50Y = 230
40(2) + 50(3) = 230
The total benefit associated with 2 units of X and 3 unit of Y is = 2160 + 3750 = $5910
Level of activity
TBx TBy MUx MUy 0 0 0 - - 1 1200 1300 1200 1300 2 2160 2550 960 1250 3 3040 3750 880 1200 4 3840 4750 800 1000 5 4560 5650 720 900Related Questions
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