✏️ L2 Practice - Consumer Choice

✏️ Kim only buys coffee and compact discs. Coffee costs $0.60 per cup, and CDs cost $12.00 each. She has $18 per week to spend on these two goods. If Kim is maximizing her utility, what is her MRS? (Put coffee on the y axis and CDs on the x axis, so the MRS will tell you how much coffee she’ll give up to get an additional CD.)

✔ Click here to view answer

We know that when you are optimizing, the IC and BC have the same slope.

• slope of IC = $-MRS$
• slope of BC = $-\frac{P_x}{P_y}$

Therefore, combining those two facts,
 $MRS=\frac{P_x}{P_y}$
Plug and chug:
$MRS=\frac{P_x}{P_y}$ $= \frac{P_{CD}}{P_{cof}}$ $=\frac{12}{.6}=20.0$

✏️ In the figure above, holding income constant, what change must have occurred to rotate the budget line from the old line (1) to the new line (2)?

1. The price of soda fell.
2. The price of pizza fell.
3. The price of pizza rose.
4. The price of soda went up.
5. (b) and (c).

✔ Click here to view answer

** **  ✅

✏️ A wheel of cheddar cheese costs Carl $40 and a night at a Broadway show costs him $100 (including the ticket and parking). When Carl maximizes his utility, his marginal utility from cheddar cheese is 8 utils. His marginal utility from a Broadway show is therefore:

1. 3.2
2. 20
3. 50
4. 500
5. None of the above

✔ Click here to view answer

** **  ✅ We’ll use the third formula on the right:

You can also let x be a broadways show instead.
$\frac{MU_B}{8}=\frac{\$100}{\$40}=2.5$
$MU_B = 2.5 × 8 = 20$

Two versions of the first optimization condition: 1. your consumption should be on the BC. 2. $X × P_x + Y × P_Y = B$ These ensure that you use all of your money.

Four versions of the second optimization condition: 1. Slope of IC = Slope of BC 2. $MRS=\frac{P_x}{P_y}$ 3. Ratio of MUs: $\frac{MU_x}{MU_y}=\frac{P_x}{P_y}$ 4. Bang for Buck: $\frac{MU_x}{P_x} = \frac{MU_y}{P_y}$ These ensure that you spend your money on the things that bring you the most utility per dollar.

Plug and chug: (help)

1. Equation:
   

   $\frac{MU_x}{MU_y}=\frac{P_x}{P_y}$

2. Plug:🔌
   

   $\frac{8}{MU_B}=\frac{\$40}{\$100}$

3. Solve: 🚂
   

   $8 × 100 = 800 = \$40 × MU_Y$
   $MU_Y = \frac{800}{40} = {20}$

4. Reflect: 🧠
   

   $\frac{8}{20} = \frac{\$40}{\$100}$
   $\frac{8}{20} = 0.4$
   $\frac{40}{100} = 0.4$

You could also have cheddar be good Y

 ✅

✏️ Suppose that you have eaten a slice of pizza and your utility is at 10 utils. You then eat two more slices of pizza and your utility rises to 14 utils. Apply the formula to calculate your MU for a slice of pizza.

# slices	# in problem	Total Utility	Additional utility from each slice
1	10	10	?
2			?
3	14	14	?

Together, the second and third slices of pizza gave us 4 utils, because we started at a total utility of 10 utils and rose to a total utility of 14 utils.

✔ Click here to view answer

$MU=\frac{ΔU}{ΔQ}=\frac{14−10}{3−1}=\frac{4}{2}=2$

Pizza

$q$	$U$	$MU=\frac{ΔU}{ΔQ}$
0	5
1	10	$\frac{(10-5)}{(1-0)}=+5$
2	13	$\frac{(13-10)}{(2-1)}=+3$
3	14	+1
4	14	+0
5	13	-1

$q$	😀
💎	😀😀	$\frac{2-0}{1-0}=2$
💎x2	😀😀😀😀	$\frac{4-2}{2-1}=2$
💎x10	😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀	$\frac{15-4}{10-2}=1.375$
💎x1000	😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀	$\frac{42-15}{1000-10}=0.0273$
💎x1000000	😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀
💎x100000000000000000000000000	😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀

Marginal utility can decrease, but as long as it is positive, my total utility will continue to increase.