Calculate the annualized inflation rate of the price of meat over the periods: (

Question

Calculate the annualized inflation rate of the price of meat over the periods: (a) May-July 1923, (b) July-September 1923, (c) October 1923,(d) November 1923.

(ii) Once per how many days did prices approximately double in Germany during this period?

May 1923: 500,000 Mark bought you 40 lbs of meat

July 1923: 10,000,000 Mark bought you 12 lbs of meat

September 1923: 10,000,000 Mark bought you 0.5 lbs of meat

October 1923: 1,000,000,000 Mark bought you 0.75 lbs of meat

November 1923: 100,000,000,000 Mark bought you 3 lbs of meat

Note: part (ii) of this question requires you to use the exponential and logarithmic functions to solve it.

Explanation / Answer

Here the inflation rate of the price of the meat over the periods can be calculated using the price of per lbs of meat that increased over the period.

(a). In May 1923, we can bought 40 lbs of meat for 500,000 Mark. So, for 1 lbs of meat, we had to pay (500,000/40) = 12,500 Mark.

In July 1923, we can buy 12 lbs of meat for 10,000,000 Mark. So, for 1 lbs of meat we had to pay (10,000,000/12) = 833,333.33 Mark.

For May-July, the price of 1 lbs of meat increases by (833,333.33 – 12,500) = 820,833.33 Mark.

So, the percentage change in price level was, (820,333.33/500,000) * 100 % = 164.07%

This is the inflation rate for May-July, 1923.

(b). Similarly, in September 1923, we can buy 0.5 lbs of meat for 10,000,000 Mark. So, for 1 lbs of meat, we had to pay (10,000,000/0.5) = 20,000,000 Mark.

Thus, for July-September 1923, the price of 1 lbs of meat increases by (20,000,000 – 833,333.33) Mark = 19,166,666.67 Mark.

So, the inflation rate for July-September was, (19,166,666.67/833,333.33) * 100 % = 2300%

(c). In October 1923, 0.75 lbs of meat could be bought for 1,000,000,000 Mark. So, the price of 1 lbs of meat for this month was, (1,000,000,000/0.75) = 1,333,333,333.33 Mark

Therefore, for October 1923, the increase in the price of meat was (1,333,333,333.33 – 20,000,000) Mark = 1,313,333,333.33.

So, the inflation rate for October 1923 was, (1,313,333,333.33/20,000,000) * 100 % = 6566.67%

(d). In November 1923, 3 lbs of meat could be bought at a price of 100,000,000,000 Mark. So, for 1 lbs of meat, a consumer had to pay, (100,000,000,000/3) = 33,333,333,333.33 Mark.

Therefore, the increase in the price level from October 1923 was, (33,333,333,333.33 – 1,333,333,333.33) Mark = 32,000,000,000 Mark.

So, the inflation rate for November 1923 was, (32,000,000,000/1,333,333,333.33) * 100 % = 2400%

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