You assume that goods are produced and sold instantaneously, which is not the case in real life. Production cycles can be as long as a few years. If the time span of your production cycle was equal to zero, then neither inflation nor deflation would have any impact on your profits (in percentages), which is what your example reveals.
Correct usage should be R_t2/W_t1, where t2 and t1 are different time moments for revenue and cost flows in a production cycle, t2 > t1. In inflation R_t2 is always greater than W_t1 (provided we were profitable before inflation set in), whereas in deflation R_t2 may become less than W_t1 (even if we were profitable before deflation set in, i.e. R > W and R/W time-invariant). That would mean a loss. So, in inflation you can never mathematically suffer a loss due to inflation per se (if you were profitable before, of course), while in deflation it becomes quite possible through the effect of deflation as such.
No. If you take into account the fact that there's a time difference between the cost of production, and the price of selling the product, you should also take into account the real interest of the blocked capital.
So if the difference in time between t1 and t2 is large enough to accumulate significant inflation or deflation, you have to take into account that the capital blocked at time t1 in the production, namely W_t1, costs you the interest on that capital between t1 and t2. So your actual benefit is not R_t2 - W_t1 but rather R_t2 - W_t1*(1+(t2-t1)*i).
If you now correct the interest rate for the inflation (that is, i = i0 + p), you will find that inflation or deflation is totally indifferent.You cannot just correct i for inflation and not correct R_t2 for it at the same time (since you would sell at higher, already inflated prices). In fact, you can't even correct it (W_t1*(1+(t2-t1)*i)) for inflation at all (since your costs are fixed at t1). You buy raw materials at old uninflated prices, and now you suggest we should recalculate their cost at new prices when we sell finished goods (that is i = i0 + p)? That would be an entirely novel idea in accounting. Strictly speaking, you can't even write R_t2 - W_t1*(1+(t2-t1)*i), or that wouldn't be your profit (or benefit, in your speak).
Nevertheless, explain to me how this can help you if you suffer
losses due to deflation? What exactly are going to correct? And what are you going to multiply the factor (R_t2 - W_t1) by if it is less than zero? Will the end result magically turn into positive?
Why should I repeat again and again that negative is negative?
To illustrate the naivity of "inflation makes for easier benefit", consider the following case:
at time t1 you buy for amount W a set of goods (say, a stock of soap).
At time t2 you sell your stock of goods for price R.
You are concluding naively that as R at t2 will be higher (because of inflation) at t2 than the price you gave for it at t1, that you will have made some benefit !!
So under inflation, storing stuff is generating a benefit under this kind of reasoning !
You immediately see where that goes wrong.
You could have placed your amount of money W on a savings account with an interest i = i0 + p at time t1.
At time t2, that amount of money would have increased by a factor (t2 - t1) * p * W simply due to inflation, which is of course EXACTLY the "benefit" you would have obtained by selling your soap.
The same is of course valid in deflation.... except that if the deflation equals i0, YOU DON'T NEED A SAVINGS ACCOUNT ANY MORE.
And THIS is the true panic that mild deflation inspires: normal people don't need a savings account any more. You don't need the financial institutions any more to compensate (partially) for the loss your money suffers under inflation. 3/4 of financial institutions are out of business under mild deflation, as they are useless.
THIS is the ONLY serious reason why politicians and financials panic for mild deflation. As others said, mild deflation and mild inflation are mirror images of one another on all other economic aspects.