Question

The market for cheap beer is characterized by the following supply and demand curves: S : q = p + 3 D : q = −2p + 24 Suppose the government puts a $3 tax on cheap beer.

1. Using the point elasticity formula, calculate the price elasticities of supply and demand at the initial equilibrium. And do you expect the incidence of the tax to fall more heavily on the consumers or the producers? Explain.

2. Calculate the effects of the tax on: (i) the price faced by consumers, (ii) the price received by producers, and (iii) the quantity traded in the market.

3. Draw a graph showing the initial equilibrium and illustrating the impact of the tax. Label all curves and axes and all relevant prices and quantities. Identify in your graph the deadweight loss and the revenue raised for the government.

Answer 1

To determine calculate the equilibrium price, we do the following :

1) Calculation of price elasticities of Demand and Supply

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2) i. The price faced by consumers = Price1 + taxes imposed

P2 = 7 + 3 = 10

ii. The price faced by producers = price2 - taxed imposed = 10 - 3 = 7

iii. Quantity Demanded after tax will reduced to 7. As shown in the below diagram.

3) The graph below shows the market for beer without tax. The equilibrium price is P1 and the equilibrium quantity is Q1. The price paid by the consumers is the same as the price received by producers.

When the tax is imposed, it drives a wedge of $3 between supply and demand, as shown in the graph below. The price paid by the consumers is P2, while the price received by producers is P2 - $3. The quantity of beer sold declines to Q2. The taxation on beer reduces its consumption, since it increases the price to consumers. As shown in the below graph, the quantity falls to Q 2 and the price rises to P2.

Graph showing deadweight Loss and tax revenues for the government