Question

2. Matilda is downloading music and videos from an online site. She is currently buying three music downloads that cost $3 each and two video downloads that also cost $3 each. The table below indicates what she reports as the marginal utility of the last music download and of the last video download in this combination of purchases.

	Quantity	Price per Download	MU per download
Music downloads	3	$3	60
Video downloads	2	$3	45

As an assignment for her Microeconomics course, Matilda used the marginal utilities that she gave to her 3^rd music download and her 2^nd video download to complete the Experiment Tally Sheet below. Her available budget was $19.00.

Downloads of	mu (score) from 1 to 100	Price of each $3.00	Money spent on	Downloads of	mu (score) from 1 to 100	Price of each $3.00	Money spent on	Total Money	Total Budget
music	mu	mu/$	music	videos	mu	mu/$	videos	Spent	Remaining
1st	?	?	$3.00	1st	?	?	$3.00	$6.00	$13.00
2nd	?	?		2nd	45	15	$3.00	$12.00	$7.00
3rd	60	20	$3.00	3rd				$15.00	$4.00
4th				4th
Total money spent on music			$9.00	Total money spent on videos			$6.00	$15.00	$4.00

1. A consumer maximizes utility when the last dollar spent on any good generates the same satisfaction as the last dollar spent on every other good. Is Matilda maximizing her utility? Explain your answer. (3 points)

2. Should Matilda consume one more video download, to move her closer to her optimum utility? Explain your answer. (3 points)

3. Should Matilda consume one less music download and one more video download, to move her closer to her optimum utility? Explain your answer. (3 points)

4. Should Matilda consume one more music download, to move her closer to her optimum utility? Explain your answer. (3 points)

Answer 1

a)

In this case, the marginal utility( additional satisfaction from consuming the last unit) of a dollar spent on music (20) is greater than the marginal utility of a dollar spent on the video. Then at this equilibrium, the consumer is not maximizing utility, because at equilibrium both marginal utilities of a dollar spent on the last unit must be the same.

b)

From the above discussion, the mathematical relationship between MUs at equilibrium is

As P_m=P_v=3,

............. (1)

To reach the optimum the above equation must reach equality. Then the LHS must decrease or the RHS must increase. Now the neoclassical theory of consumer choice assumes diminishing marginal utility of good. That is the marginal utility from every additional unit consumed of a good decrease with each additional unit. Then consuming one more video with a decrease in the MU of video and the RHS will decrease further.

Therefore, the consumer should not consume one more video download.

c)

According to equation (1) above, one less music download will increase MU_m and one more video download decreases MU_v further. Then LHS increases and the RHS decreases to strengthen the inequality further.

Therefore, the consumer should not consume one less music download and one more video download.

d)

According to equation (1) above, one more music download will decrease MU_m. Then buying one more music download decreases LHS to drive the inequality towards equality.

Therefore, the consumer should consume one more music download to reach optimum.