Question

3. The table below shows Bob’s total utility from apples and oranges. Assume that Bob has $160 to spend on apples and oranges each month (whole units). Oranges cost $16 each, and apples cost $40 each.

1. Fill in the figures for marginal utility and marginal utility per dollar for both oranges and apples.

2. Are these preferences consistent with the law of diminishing marginal utility? Explain briefly.

3. Given the budget of $160, what quantity of apples and what quantity of oranges will maximize Bob’s level of satisfaction? Explain

4. Draw the budget constraint (put apples on the horizontal axis) and identify the optimal combination of apples and oranges as point A.

5. Now suppose the price of apples falls to $20.Which of the columns in the table must be recalculated? Do the required recalculations.

6. After the price change, how many oranges and how many apples will Bob purchase?

7. Draw the new budget constraint and identify the new optimal combination of apples and oranges as point B.

8. Did a decrease in the price of apples cause Bob to buy more oranges and apples? If so, why?

            Oranges                                             Apples

NO      TU      MU     MU/$              NO      TU     MU    MU/$

1. 100      __      __                   1         44       __       __
2. 160      __       __                   2         84       __       __
3. 200     __       __                   3         104     __       __
4. 220     __       __                   4         114      __       __
5. 232     __       __                   5         120      __       __
6. 242     __       __                   6         124      __       __
7. 246     __       __                   7         126      __       __

           

Answer 1

BIB consumes only two goods apples and oranges. He has $160 which he can spend on apples and oranges. The price of apple is $40 and price of oraange is $16. The total utility from oranges and apples are given below:

Oranges:

No	TU	MU	MU/S
1	100	100	100/16=6.25
2	160	60	60/16=3.75
3	200	40	40/16=2.5
4	220	20	20/16=1.25
5	232	12	12/16=0.75
6	242	10	10/16=0.625
7	246	4	4/16=0.25

Apples:

No	TU	MU	MU/S
1	44	44	44/40=1.1
2	84	40	40/40=1
3	104	20	20/40=1/2=0.50
4	114	10	10/40=1/4=0.25
5	120	6	6/40=0.15
6	124	4	4/40=0.1
7	126	2	2/40=0.05

b. Yes the preferences are consisitent with diminishing marginal utility as with each additional unit of consumption of apple or orange, the marginal utility is falling.

c. The utility will be maximised where bob utiised all the money and where marginal utility from a dollar is equal for apples and oranges. So he will buy 5 units of oranges and 2 units of apples.

d. The budget constraint and equilibrium is shown below:

e. When price of apple fall to $40, the marginal utility per dollar will change. The calcuation is shown below:

No	TU	MU	MU/S
1	44	44	44/20=2.2
2	84	40	40/20=2
3	104	20	20/20=1
4	114	10	10/20=0.5
5	120	6	6/20=0.30
6	124	4	4/20=0.2
7	126	2	2/20=0.1

f. After the price change, bob will buy 5 oranges and 4 apples.

g. The budget constraint and equilibrium is shown below:

h. Yes, As the price of apples fall, the real income of bob has increased so he will consume more units of apples. He will not buy more oranges as subsitution effect cancels out the income effect.