Question

1. Consider the following utility data for some hypothetical consumer:

Q	TUApples	TUOranges
0	0	0
1	40	45
2	60	75
3	72	102
4	82	120
5	88	135
6	90	145
7	91	148

Use this data to assist you in answering the following questions:

What is the optimal consumption bundle when apples are $2 and oranges are $3? Assume this individual's spending is constrained by his income, which is $10. Show this using a budget constraint and indifference curve.

Answer 1

Utility maximizing condition is when marginal utility per dollar is equal for both goods.

Price of apple , Pa = $2

Price of orange ,Po = $3

Q	TUa	MUa=Change in TUa	MUa/Pa=MUa/$2	TUo	MUo=Change in TUo	MUo/Po= MUo/$3
0	0	-	-	0	-	-
1	40	40	20	45	45	15
2	60	20	10	75	30	10
3	72	12	6	102	25	9
4	82	10	5	120	18	6
5	88	6	3	135	15	5
6	90	2	1	145	10	3.33
7	91	1	0.5	148	3	1

We can see from the above table that when Quantity of apples = 2 and quantity of oranges = 2 , MUa/Pa= MUo/Po = 10. And ($2)(2)+($3)(2)= $10 (i.e equal to income) .This means the utility maximizing bundle or optimal bundle is 2 apples and 2 oranges which satisfies the budget constraint.

Budget constraint : PaA+ PoO = I

2A + 3O = 10

When A=0 , O=3.33

When O=0, A= 5

By plotting this we get the budget constraint and indifference curve is tangent to the budget line at the optimal bundle as shown in the graph below: