Let's consider the effects of inflation in an economy composed of only two people: bob, a bean farmer, and rita, a rice farmer. bob and rita both always consume equal amounts of rice and beans. in 2013, the price of beans was $1, and the price of rice was $3. suppose that in 2014 the price of beans was $2 and the price of rice was $6. what was inflation? was bob better off, worse off, or unaffected by the changes in prices? what about rita?

b. now suppose that in 2014 the price of beans was $2 and the price of rice was $4. what was inflation? was bob better off, worse off, or unaffected by the changes in prices? what about rita?

c. finally, suppose that in 2014 the price of beans was $2 and the price of rice was $1.50. what was inflation? was bob better off, worse off, or unaffected by the changes in prices? what about rita?

d. what matters more to bob and rita�the overall inflation rate or the relative price of rice and beans?

See below.

Explanation:

Lets first calculate inflation using the formula for Consumer Price Index

Inflation for a good = (Year 2 price - Year 1 price / Year 1 price) * 100

Using the above formula we can calculate inflation when Beans = $2 and Rice = $6.

Inflation for Beans = (2-1/1) * 100 = 100%

Inflation for Rice = (6-3/3) * 100 = 100%

Since each of them use rice and beans in equal proportions we assign them weights of 0.5 each,

Inflation Total = 0.5 * 100 + 0.5 * 100 = 100%

We assume Bob and Rita form a transnational relation and as such neither is worse off because the exchange rate between them remains the same,

Exchange rate before inflation = 3/1 = 3, Bob can buy 1 Rice by selling Rita 3 Beans.

Exchange rate after inflation = 6/2 = 3, so Bob can still buy 1 Rice by selling Rita 3 Beans.

B) For Prices 2 and 4 we use the above formulas,

Total Inflation = (2-1/1)*100*0.50 + (4-3/3)*100*0.50 = 66.66%

Bob is better off and Rita Worse off as the exchange rate for Bob has improved He can acquire 1 Rice for 4/2 = 2 Beans instead of 3 he needed before. Rita needs to sell him more to maintain her consumption but since they always consume same amount, she is worse off.

C) For Prices 2 and 1.5.

Total Inflation = (2-1/1)*100*0.50 + (1.5-3/3)*100*0.50 = (50-25) = 25%

Bob is now worse off and Rita better off as the Exchange rate change has favored Rita. Rita now only needs to sell 1 rice to obtain 2/1.5 = 1.3 units of Beans. Bob will have to sell more to maintain his initial consumption level.

D)

Bob and Rita are more concerned with their rate of exchange which is the change in real terms. As long as the changes are proportional and there are no third actors in the economy model, the 2 agents are not affected at all. What matters to them is their transnational rate and not inflation on the whole in this case.

Hope that helps.