In Case You Doubt

You might doubt that declining dollar prices of shoes (caused by increased production) accompanied by fixed dollar prices of wheat (resulting from fixed production of wheat) equals the same product to product relationship as the ratios (prices) under direct exchange. It does not seem intuitively obvious.

I had my doubts too; so I ran this table:

Shoe production increases by 2% per month.
Wheat production does not increase
					Conversion: Dollar to Direct Exchange Prices
	Direct Exchange Prices		Dollar Prices		dollar price of wheat / dollar price of shoes	dollar price of shoes / dollar price of wheat
Time (Month)	shoe to wheat price	wheat to shoes price	dollar price of shoes	dollar price of wheat	shoe to wheat price	wheat to shoes price
10	0.481	2.079	11.548	5.556	0.481	2.079
20	0.501	1.997	11.096	5.556	0.501	1.997
30	0.521	1.919	10.661	5.556	0.521	1.919
40	0.542	1.844	10.243	5.556	0.542	1.844

Take the 30th month as an example:

(dollar price of wheat) / (dollar price of shoes) = pair of shoes / bushel of wheat

$5.556 / $10.661 = 0.521 pair of shoes / bushel of wheat

(dollar price of shoes) / (dollar price of wheat) = bushels of wheat / pair of shoes

$10.661 / $5.556 = 1.919 bushels of wheat / pair of shoes

Now, let's move on to examine the effects of inflation.