Question

In a small country near the Baltic Sea, there are only three commodities: potatoes, meatballs, and jam. Prices have been remarkably stable for the last 50 years or so. Potatoes cost 2 crowns per sack, meatballs cost 4 crowns per crock, and jam costs 6 crowns per jar. (a) Write down a budget equation for a citizen named Gunnar who has an income of 360 crowns per year. Let P stand for the number of sacks of potatoes, M for the number of crocks of meatballs, and J for the number of jars of jam consumed by Gunnar in a year. . (b) The citizens of this country are in general very clever people, but they are not good at multiplying by 2. This made shopping for potatoes excruciatingly difficult for many citizens. Therefore it was decided to introduce a new unit of currency, such that potatoes would be the numeraire. A sack of potatoes costs one unit of the new currency while the same relative prices apply as in the past. In terms of the new currency, what is the price of meatballs? . (c) In terms of the new currency, what is the price of jam? . (d) What would Gunnar’s income in the new currency have to be for him to be exactly able to afford the same commodity bundles that he could afford before the change? . (e) Write down Gunnar’s new budget equation. Is Gunnar’s budget set any different than it was before the change?

Answer 1

(a)
`360=2 * P + 4 * M + 6 * J`

(b) 2

(c) 3

(d) 180

(e)
`180=1 * P+ 2 * M + 3 * J`

It is not different than before, he can afford the same amount of goods.

Step-by-step explanation:

let's start by writing down all the components of the problem:

1. Potato's sacs (
`P`) cost 2 crowns, denote the price a potato sack by
`P_p`

2. Meatballs (
`M`) cost 4 per crock, denote
`P_m` as the price of meatballs

3. Jam cost 6 per jar (
`J`), denote
`P_j` as the price of jam.

4. Gunnar has an Income
`M=360\\`

His budget constrain is then:

• The amount he spends in potatoes
  `P_p* P`
• The amount he spends in meatballs
  `P_m * M\\`
• The amount he spends in jam
  `P_j * J`

He only spends money on those goods, then his expenditures equals his income

`I=P_p * P + P_m * M + P_j * J`

`360=2 * P + 4 * M + 6 * J`

(b) Next we need to re express all prices so relative prices are the same as before.

If the new price of potatoes is
`P'_p=1`, then the price of meatballs will be
`P'_m=(P_m)/(P_p)=(4)/(2)=2`

(c) the same can be done for jam

If the new price of potatoes is
`P'_p=1`, then the price of jam will be
`P'_j=(P_j)/(P_p)=(6)/(2)=3`

(d) Gunnar's Income would be then half as before

`I'=(I)/(P_p)=(360)/(2)=180`

(e) We can summarize everything re expressing Gunnars budget constraint

The old budget constraint was

`I=P_p * P + P_m * M + P_j * J`

Now setting
`P'_p=1` is the same as dividing everything by
`P_p=2`

`(I)/(P_p)=(P_p)/(P_p) * P + (P_m)/(P_p) * M + (P_j)/(P_p) * J`

`I'= P + P'_m * M + P'_j * J`

`180=1 * P+ 2 * M + 3 * J`