Recall the case where the government imposes a fixed tax per unit sold. That is, if a consumer pays p for a good, the firm has to pay t to the government and keeps p − t for itself. Assume that the market demand function is strictly decreasing, that the market supply function is strictly increasing, and that both these functions are continuous. Let p∗ denote the equilibrium price of the good before tax and p∗∗ denote the equilibrium price that consumers pay for the good after the tax t. Show that p∗∗ − p∗ < t. That is, the change in price that consumers must pay is less than the amount of the tax.

Notes and hints: this is a hard-ish problem. It might be helpful to proceed by contradiction. That is, assume that the conclusion you want to obtain (i.e. p∗∗ − p∗ < t) is false, and then show that this leads to a logical contradiction. Therefore, it must be that our conclusion is true. that is, p∗∗ − p∗ < t.

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Since the demand and supply curve is continious therefore Demand Function QD a bP Sup... View the full answer