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Finding the optimal allocation of budget

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Suppose a firm is considering two different activities, activities X and Y, which yield
the following schedule of total benefits shown below. The price of X is $2 per unit and the price of Y is $10 per unit.

Total benefit of Total benefit of
Level of Activity Activity X Activity Y
_________________________________________________________
0 0 0
1 $30 $100
2 54 190
3 72 270
4 84 340
5 92 400
6 98 450

A. The firm places a budget constraint of $26 on expenditures on activities X and
Y. What is the level of activity that maximizes the total benefit subject tot he budget constraint? What is the total benefit if your solution is implemented?

B. Suppose that the budget increases to $58. What is the optimal level of activity
X and Y now? What is the total benefit when the budget is $58?

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Solution Summary

Solution describes the steps to calculate optimal allocation of expenditure on the given activities.

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Please refer attached file for tables.

A. The firm places a budget constraint of $26 on expenditures on activities X and Y. What is the level of activity that maximizes the total benefit subject tot he budget constraint? What is the total benefit if your solution is implemented?

Marginal benefit per dollar spent on X (MBx/Px) is $15 for activity level 1, which is higher than that of Y i.e. $10.
So, first activity level of X should be chosen first.

Now let us see activity level 2 for X. In this case marginal benefit per dollar spent is 12, which is higher than marginal benefit per dollar
spent for first activity level of Y. So, second activity level of X should be chosen next.

Now let us see activity level 3 for X. In this case marginal benefit per dollar spent is 9, which is lower than marginal benefit per dollar
spent ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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