Price Producers Receive as a Result of Indirect Taxes In my economics class, we were introduced to the idea that if the government imposes an indirect tax on a good, the price consumers have to pay increases, but along with this increase in price for consumers, the price producers receive decreases. I understand the former perfectly, however, don't understand why the price producers receive decreases.



$P^*$ is the original price prior to the imposition of taxes, and $Q^*$ is the quantity demanded prior to the imposition of taxes. $P_c$ is the price paid by consumers after the government's decision, and $P_p$ is the price received by firms, once again, after the imposition of taxes. 

My question is, why isn't $P^*$ equal to $P_p$?
The idea is that both the consumer and the producer of a good take on some of the burden of a tax, even if you don't intend to levy the tax on one or the other. So if you have a sales tax that consumers have to pay, what will happen is that consumers won't take the full brunt of that tax. They will demand less and producers will have to make the product cheaper in response, so they get less revenue overall anyway.

How much tax burden each side will have to pay depends on their relative elasticities, which I imagine you'll be going over soon if you're going over tax incidence. Elasticity is a measure of sensitivity to a change in price to in this case, quantity supplies or demanded.

So $P* \neq P_p$ because the producer will have to shift from the equilibrium just like the producer will have to. It's the same idea for the consumer as for the producer, since the tax burden falls on both of them.