Consumption Taxes Vs. Production Taxes
In his chapter on sales taxes (the same logic applies to value added taxes) in Power & Market, he argues:
"Prices, however, are never determined by costs of production, but rather the reverse is true. The price of a good is determined by its total stock in existence and the demand schedule for it on the market. But the demand schedule is not affected at all by the tax. The selling price is set by any firm at the maximum net revenue point, and any higher price, given the demand schedule, will simply decrease net revenue. A tax, therefore, cannot be passed on to the consumer......
....It should be quite evident that if businesses were able to pass tax increases along to the consumer in the form of higher prices, they would have raised these prices already without waiting for the spur of a tax increase. Businesses do not deliberately peg along at the lowest selling prices they can find. If the state of demand had permitted higher prices, firms would have taken advantage of this fact long before. It might be objected that a sales tax increase is general and therefore that all the firms together can shift the tax. Each firm, however, follows the state of the demand curve for its own product, and none of these demand curves has changed. A tax increase does nothing to make higher prices more profitable."
There are two key fallacies with this analysis. First, it is not true that firms typically try to maximize revenues, they attempt to maximize profits. What this means in practice is that they will set the price which creates the highest possible gross profit, given a certain level of fixed costs assuming that fixed costs are lower than gross profits (If fixed costs are higher, than the firm will go bankrupt after a while). Gross profit is defined as revenues minus variable costs.
In practice, the distinction between fixed and variable costs isn't always as clear-cut as there also exist semi-variable costs, but introducing them doesn't change the point of the analysis for this context, it only makes it more complicated so for simplicity I will assume only fixed and variable costs.
Anyway, returning to the issue of profit-maximization given a certain level of fixed costs, it should be clear that maximum gross profit is reached at the point where further price increases will increase gross profit per unit (margins) by less than it will decrease volume sales, and where price cuts would reduce gross profit per unit by less than it will increase volume sales. To use a concrete example, take a firm which sells a certain product for say $40 per unit and which has variable costs of $32, and which has a volume sale of 100,000 units. At this point, gross profit is $800,000 (($40-$32)*100,000). If it is assumed that a $1 increase in price will lower sales by 12%, and that a $1 cut in prices will increase sales by 12%, then $40 is also the profit-maximizing point as a $41 price would create a gross profit of only $792,000 (($41-$32)*(0.88*100,000)), and as a $39 price would create a gross profit of only $784,000 (($39-$32)*(1.12*100,000)).
Consider then what will happen if the government slaps a 12,5% sales tax on the product, and the product is equally price sensitive as before. Then at a $40 price, gross profits would only be approximately $355,556 ((($40/1.125)-$32)*100,000). Cutting the price to $39 would have an even more disastrous effect on profits, reducing it to only $298,667 ((($39/1.125)-$32)*(1.12*100,000). By contrast, raising the price to $41 would now increase gross profits to approximately $391,111 ((($41/1.125)-$32)*88,000). Because of the reduction in gross profit per unit given a certain price that the tax causes, then the profit maximizing price will be pushed upward even assuming unchanged price sensitivity.
Moreover, there are reasons to assume that price sensitivity will fall as a result of this tax. Contrary to what Rothbard asserts the demand curve for individual firms have in fact changed. The reason is that the demand curve for an individual firm is determined in part by how tough competition the firm faces. If an individual firm raises its prices, while others don't then consumers will switch to those other firms to a much higher extent than if all companies raise their price. If both Toyota and GM raises their price by an equal magnitude, then there is not any point in going over to the other company to avoid price increases. If only Toyota raises its price, it would by contrast make more sense to consider going over to GM. And because the profit maximizing price have as we saw above increased even overlooking any change in price sensitivity, then all companies are in fact likely to raise their price.
So, because the consumption tax means that a price increase would increase margins more than before while at the same time reduce the reduction in volume sales, it should be very clear that the tax can and will raise the price and therefore hit consumers.
However, while Rothbard was wrong in stating that consumption taxes will not raise prices, he was right that production taxes (for example income taxes and payroll taxes) will have the same effect on prices as consumption taxes. At least, as we shall see, with regard to domestic producers that sells to domestic consumers and also assuming the absence of transfer payments. Production taxes will, at least in the long run, have identical effects on prices as they too reduce margins, and therefore both by the direct margin reducing effect and the indirect effect of reducing competitive pressure they will raise prices.
And so, in a completely closed economy, with for example a hypothetical world government or with a completely isolated economy like North Korea (almost) is, then it wouldn't matter whether the government would receive its revenues through taxes labeled as production taxes or taxes labeled as consumption taxes. Both would reduce production and therefore also purchasing power, which given a certain money supply would also raise prices.
However, there two ways in which the structure of taxation could matter. One is if we assume that not all people receive their income through production. If for example some people receive hand-outs from the government and if these hand-outs are unaffected by the change in the structure of taxation then a shift from production taxes to consumption taxes would redistribute from receivers of government hand-outs to producers (or more correctly, it would result in reduced redistribution from producers to the receivers of hand-outs). That is because the receivers of the hand-outs pay consumption taxes too, meaning that given a revenue neutral shift in taxation, this will reduce taxes on producers. However, if receivers of government hand-outs are compensated this effect will not appear.
Another effect from a shift from production taxes to consumption taxes would be to increase net exports and reduce domestic demand. The reason for this is that production taxes hits exports, but not imports. By contrast, consumption taxes hits imports, but not exports. The sharp increase in the German trade- and current account surplus in 2007 after Germany raised its VAT and at the same time reduced payroll taxes illustrates this effect.