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.