Question

what will be the budget allocation? WORK IT OUT w LaunchPad interactive activity 16. Answer the questions following the table. First-Run Movies Bottles of Wine Quantity Total Utility Marginal Utility Marginal Utility Quantity Total Utility O 140 180 260 N 340 360 W 460 440 510 500 0 540

Answer 1

a.

MOVIES			WINE
Qty	TU	MU	Qty	TU	MU
0	0	NIL	0	0	NIL
1	140	140	1	180	180
2	260	120	2	340	160
3	360	100	3	460	120
4	440	80	4	510	50
5	500	60	5	540	30

MU = $\Delta TU/\Delta Q$

b. For utility maximization, the MU of the last dollar spent on each good should be the same, that is, MU per dollar = MU/price.

MUm/P	MUw/P
nil	nil
14	18
12	16
10	12
8	5
6	3

Thus 2 units of movie and 3 units of wine would be consumed.

c. Now since the price of wine changed, so the MU per $ would be = MU / 5

MUw/P

nil

36

32

24

10

6

Now the equilibrium is when the MU per $ is same, which is at 10 and 6.

When MU per $ is 10, total cost = 3 * 10 + 4 * 5 = $50.

When MU per $ is 6, total cost = 5 * 10 + 5 * 5 = $75. (exceeds budget)

3 units of movies and 4 units of wine would thus be equilibrium allocation.

d. PED = $\frac{Q2-Q1}{(Q2+Q1)/2}\div \frac{P2-P1}{(P2+P1)/2}$

When Price = $10, Quantity = 3

When Price = $5, Quantity = 4

PED = $\frac{4-3}{(4+3)/2}\div \frac{5-10}{(10+5)/2}$

PED = 0.2857/-0.667

PED = -0.4283