1. Lectures in Microeconomics-Charles W. Upton
Budget Constraints
Lectures in Microeconomics-Charles W. Upton

2. More on the Theory of Choice
We have talked about indifference curves to represent a consumer’s preferences.
That is not all of the story. Budget realities play a role.
Budget Constraints

3. Apples and Bananas A 4 5 7 3 I3 8 2 \ I2 6 1 I1 B
Budget Constraints

4. Marginal Rate of Substitution
U = AB
In this example, the following points lie on a single indifference curve:
Apples 16 8
5.33 4
3.2
2.67
Bananas 1 2 3 5 6
Budget Constraints

5. Marginal Rate of Substitution
U = AB
In this example, the following points lie on a single indifference curve:
Apples 16 8
5.33 4
3.2
2.67
Bananas 1 2 3 5 6
Budget Constraints

6. Marginal Rate of Substitution
U = AB
In this example, the following points lie on a single indifference curve:
Apples 16 8
5.33 4
3.2
2.67
Bananas 1 2 3 5 6
Budget Constraints

7. Marginal Rate of Substitution
How many apples is our consumer willing to substitute for an additional banana?
Apples 16 8
5.33 4
3.2
2.67
Bananas 1 2 3 5 6
MRS
8.00
1.33
0.80
.053
Budget Constraints

8. Marginal Rate of Substitution
How many apples is our consumer willing to substitute for an additional banana?
Apples 16 8
5.33 4
3.2
2.67
Bananas 1 2 3 5 6
MRS
8.00
1.33
0.80
.053
Budget Constraints

9. Declining MRS
MRS is declining. With more bananas, the number of apples you will give up to get another banana declines
Apples 16 8
5.33 4
3.2
2.67
Bananas 1 2 3 5 6
MRS
8.00
1.33
0.80
.053
Budget Constraints

10. MRS and Indifference Curves
The Slope of the Indifference Curve gives us the MRS B
Budget Constraints

11. MRS and Indifference Curves
As we move along the indifference curve, the principle of diminishing MRS means a diminishing slope B
Budget Constraints

12. The Budget Constraint
Indifference curves, such as shown on the right, tell us about preferences A B
Budget Constraints

13. The Budget Constraint
Indifference curves, such as shown on the right, tell us about preferences
There is another part of the story, the budget constraint A B
Budget Constraints

14. The Budget Constraint Suppose apples sell for pA; bananas for pB

15. The Budget Constraint Suppose apples sell for pA; bananas for pB
The consumer has income Y
Budget Constraints

16. The Budget Constraint paA + pbB = Y
Suppose apples sell for pA; bananas for pB
The consumer has income Y
paA + pbB = Y
Budget Constraints

17. The Budget Constraint paA + pbB = Y paA + pbB - paA= Y- paA
Suppose apples sell for pA; bananas for pB
The consumer has income Y
paA + pbB = Y
paA + pbB - paA= Y- paA
Budget Constraints

18. The Budget Constraint paA + pbB = Y paA + pbB - paA= Y- paA
Suppose apples sell for pA; bananas for pB
The consumer has income Y
paA + pbB = Y
paA + pbB - paA= Y- paA
pbB = Y- paA
Budget Constraints

19. The Budget Constraint 1/pb(pbB) = 1/pb(Y-paA)
Suppose apples sell for pA; bananas for pB
The consumer has income Y
paA + pbB = Y
paA + pbB - paA= Y- paA
pbB = Y- paA
1/pb(pbB) = 1/pb(Y-paA)
Budget Constraints

20. The Budget Constraint B = (1/pb)Y – (pa/pb)A
Suppose apples sell for pA; bananas for pB
The consumer has income Y
paA + pbB = Y
paA + pbB - paA= Y- paA
pbB = Y- paA
1/pb(pbB) = 1/pb(Y-paA)
B = (1/pb)Y – (pa/pb)A
Budget Constraints

21. Graphing The Budget Constraint
If we spend everything on bananas, we can buy Y/pb bananas.
If we spend everything on apples, we can buy Y/pa apples
B = (1/pb)Y – (pa/pb)A A
Y/pa B
Y/pb
Budget Constraints

22. Constrained Maximization
Look at three possible choices: 1, 2, and 3
1 is the best, but we cannot afford it
We can afford 2 and 3, but 2 lies on a higher indifference curve A
Y/pa 1 2 3 B
Y/pb
Budget Constraints

23. Constrained Maximization
In fact, given the budget, 2 is the best we can do.
This choice maximizes utility subject to the budget constraint A
Y/pa 1 2 3 B
Y/pb
Budget Constraints

24. The Budget Constraint
At the utility-maximizing point, the budget line is just tangent to the indifference curve. A
Y/pa 1 2 3 B
Y/pb
Budget Constraints

25. The Budget Constraint
At the utility-maximizing point, the budget line is just tangent to the indifference curve.
It just touches the curve. A
Y/pa 1 2 3 B
Y/pb
Budget Constraints

26. MRS and MRT
Budget Constraints

27. MRS and MRT
The Marginal Rate of Substitution (MRS) is the rate at which we will substitute bananas for apples.
Budget Constraints

28. MRS and MRT
The Marginal Rate of Substitution (MRS) is the rate at which we will substitute bananas for apples.
The Marginal Rate of Transformation (MRT) is the rate at which we can substitute bananas for apples.
Budget Constraints

29. MRS and MRT
The Marginal Rate of Substitution (MRS) is the rate at which we will substitute bananas for apples.
The Marginal Rate of Transformation (MRT) is the rate at which we can substitute bananas for apples.
Budget Constraints

30. MRS and MRT Utility maximization requires that MRS = MRT
Budget Constraints

31. MRS and MRT Utility maximization requires that MRS = MRT
Why? Suppose pa = 50¢ and pb = 10¢
Budget Constraints

32. MRS and MRT Utility maximization requires that MRS = MRT
Why? Suppose pa = 50¢ and pb = 10¢
MRT = 50¢/10¢ = 5
Budget Constraints

33. MRS and MRT Utility maximization requires that MRS = MRT
Why? Suppose pa = 50¢ and pb = 10¢
MRT = 50¢/10¢ = 5
Suppose MRS = 4. That is, I would be willing to take four bananas for one apple.
Budget Constraints

34. Sell an apple, buy five bananas and be better off
MRS and MRT
Sell an apple, buy five bananas and be better off
Utility maximization requires that
MRS = MRT
Why? Suppose pa = 50¢ and pb = 10¢
MRT = 50¢/10¢ = 5
Suppose MRS = 4. That is, I would be willing to take four bananas for one apple. .
Budget Constraints

35. MRS and MRT
Suppose MRS = 6. That is, I would be willing to take six bananas for one apple.
Budget Constraints

36. MRS and MRT
Suppose MRS = 6. That is, I would be willing to take six bananas for one apple.
Another way of putting that is that I would be willing to give up six bananas for one apple’
Budget Constraints

37. Sell five bananas, get another apple and be better off
MRS and MRT
Suppose MRS = 6. That is, I would be willing to take six bananas for one apple.
Another way of putting that is that I would be willing to give up six bananas for one apple.
Sell five bananas, get another apple and be better off
Budget Constraints

38. End
©2004 Charles W. Upton
Budget Constraints