✏ "JoAnne's Books vs. Movies" Example

Part a.

✏️ JoAnne is trying to decide how many books and how many movies to consume each month. She has $136 to spend on the two goods. Movies cost $8 each, and books cost $20 each. Each good can only be purchased in whole numbers (not fractions of a good).

JoAnne’s preferences for movies and books are summarized by the following table:

Movies				Books
No. per Month	Total Utility	Marginal Utility	MU/$	No. per Month	Total Utility	Marginal Utility	MU/$
1	50			1	22
2	80			2	42
3	100			3	52
4	110			4	57
5	116			5	60
6	121			6	62
7	123			7	63

Fill in the figures for marginal utility and for marginal utility per dollar spent for both movies and books.

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Marginal Utility for Movies:
MU of first movie: MU = $\frac{50 \text{ utils} - 0 \text{ utils}}{1 \text{ movie} - 0 \text{ movies}} = 50 \text{ utils}$
* he assumes the total utility of 0 movies is 0 - sometimes this is a convenient assumption, but we don’t generally make it.
MU of second movie: MU = $\frac{80 \text{ utils} - 50 \text{ utils}}{2 \text{ movies} - 1 \text{ movie}} = 30 \text{ utils}$
MU of third movie: MU = $\frac{100 \text{ utils} - 80 \text{ utils}}{3 \text{ movies} - 2 \text{ movies}} = 20 \text{ utils}$

MU/$ for Movies: ($P_M = \$8$)
1 movie per month: $MU/\$ = \frac{50 \text{ utils}}{\$8} = 6.25 \text{ utils/\$}$
2 movies per month: $MU/\$ = \frac{30 \text{ utils}}{\$8} = 3.75 \text{ utils/\$}$
3 movies per month: $MU/\$ = \frac{20 \text{ utils}}{\$8} = 2.5 \text{ utils/\$}$

MU/$ for Books: ($P_B = \$20$)
1 book per month: $MU/\$ = \frac{22 \text{ utils}}{\$20} = 1.1 \text{ utils/\$}$

Movies				Books
No. per Month	Total Utility	Marginal Utility	MU/$	No. per Month	Total Utility	Marginal Utility	MU/$
1	50	50	6.25	1	22	22	1.10
2	80	30	3.75	2	42	20	1.00
3	100	20	2.50	3	52	10	0.50
4	110	10	1.25	4	57	5	0.25
5	116	6	0.75	5	60	3	0.15
6	121	5	0.63	6	62	2	0.10
7	123	2	0.25	7	63	1	0.05

Part b.

✏️ Do JoAnne’s preferences exhibit diminishing marginal utility for both goods? Why or why not?

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Movies				Books
No. per Month	Total Utility	Marginal Utility	MU/$	No. per Month	Total Utility	Marginal Utility	MU/$
1	50	50	6.25	1	22	22	1.10
2	80	30	3.75	2	42	20	1.00
3	100	20	2.50	3	52	10	0.50
4	110	10	1.25	4	57	5	0.25
5	116	6	0.75	5	60	3	0.15
6	121	5	0.63	6	62	2	0.10
7	123	2	0.25	7	63	1	0.05

As you can see from the table above, the marginal utility of movies decreases as she consumes more movies. Likewise, the marginal utility of books decreases as she consumes more books. Therefore, her preferences exhibit diminishing marginal utility for both goods.

Part c.

✏️ > Given her budget of $136, what quantity of books and what quantity of movies will maximize JoAnne’s utility? Explain how you arrived at your answer.

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To answer this question, we have to find a basket of goods where she is satisfying the two conditions for a consumer optimum.

But how do we find this basket of goods? You could try guessing. Obviously, a good starting point is that you need to think about how she will spend all of her budget. You might have some good luck this way.

Here’s my favorite way to do it. What I do is I go through and I imagine I’m her. I then think about the first thing I would buy. Bang for the buck, in other words marginal utility per dollar, tells me how good of a value something is. Naturally, the first thing that I would put into my shopping cart is the thing with the highest marginal utility per dollar. Once I got that in my shopping cart, I notice that I still have money left, so I put another item in my shopping cart. As before, I choose the item with the highest marginal utility per dollar. I will keep going through and keep on adding things to my shopping cart until I run out of money. If you follow this process through to completion, you will find the basket of goods that satisfies both conditions for a consumer optimum.

Movies				Books
No. per Month	Total Utility	Marginal Utility	MU/$	No. per Month	Total Utility	Marginal Utility	MU/$
1	50	50	6.25	1	22	22	1.10
2	80	30	3.75	2	42	20	1.00
3	100	20	2.50	3	52	10	0.50
4	110	10	1.25	4	57	5	0.25
5	116	6	0.75	5	60	3	0.15
6	121	5	0.63	6	62	2	0.10
7	123	2	0.25	7	63	1	0.05