A hypothetical question on neutrality of money Let's assume that we start with an economy producing two goods, A and B, with each priced $100. Each good is weighted using the same quantity, so CPI equals 100. Nominal wage is also 100 dollars. An increase in money supply cause an equal increase of 20% for both good A and good B, while real wage fall because that CPI now equals 120. The question is that, relative prices between A and B did not change while the real wage fell (against CPI), what would be the result of these on real GDP? I presume that the producers would want produce the same amount as their relative prices did not change while the workers would reduce their quantity supplied as their real wage fell, compared to CPI. Thus, this would bid up wages until equilibrium in labor market is reached, as firms would find it non-optimal supplying any other quantity than initial level of real GDP because their MC would be bigger than their MR or vice versa. 

Did I got the situation right? Any thoughts? Thanks in advance.
I think I figured out the answer using Excel. I assumed that there was a 100% inflation in goods market so that the prices of two goods doubled, while keeping the nominal wage fixed. The result was that an individual producer would still be making positive inflation adjusted profits. So I assume that in the scenario I described above, real GDP would still increase even though relative prices in goods market stays the same because that costs adjusted for inflation fall. When I also doubled the nominal wage so that the equilibrium in labor market is back to its initial level, profits were down back to the initial levels.

Here are the screenshots from Excel



A hypothetical firm and its cost curve.



Real price and real cost of the firm after a 100% inflation in the goods market.



Inflation adjusted profits of the firm after doubling the nominal wage from 120 dollars to 140 dollars. Profit levels are returned to their initial amounts and I presume that at this point firms would go back to produce the initial amount of real GDP.

I think what I got incorrect was that I was trying to compute real wages by dividing it to a ratio of nominal prices to CPI using the formula (W)/(P/P*) where P* representing CPI level. The correct usage should be (W/P*)/(P/P*) so that an equal increase in price of an individual good and CPI while holding the nominal wage fixed should result in a lower real wage, inducing higher profits than the initial level of prices and costs thus resulting in more labor demanded by the firm producing good A. 

When I doubled the nominal wage and used the (W/P*)/(P/P*) formula, real wage went back to the initial level so that there was no profit opportunity so the firms reduced the extra real GDP supplied and therefore went back to their original levels of production.