Question

1 Standard Model of Taxes Consider the standard supply and demand model shown in 1. The demand curve in the figure is given by PD 10-Q. One interpretation of demand curves is that they show the willingness to pay of the marginal consumer. For example, the willingness to pay of the person who buys the 5th unit is 10-5-5. The supply curve is given by PS Q. We saw in EC311 that supply curves are interpretable as the marginal cost of producing each unit sold in the market. Figure 1: Basic Model of Supply and Demand Quantity Demand Supply Notes. This figure shows the basic supply and demand model

Answer 1

1.1 Demand P^D = 10 - Q = Marginal revenue MR

Also, Supply P^S = Q = Marginal cost MC

Therefore, for equilibrium , MR = MC

or, 10-Q=Q

or, Q = 10/2 = 5

and P = Q = $5

1.2 Consumer surplus = area below demand curve above equilibrium price =1/2 * equilibrium quantity * (price charged when quantity produced is zero - equilibrium price)

or, consumer surplus = 1/2*5*(10-5) = 1/2*5*5 = 12.5

Similarly, Producer surplus = area above supply curve below equilibrium price = 1/2 * equilibrium quantity * (equilibrium price - price charged when quantity supplied is zero)

or, producer surplus = 1/2 * 5 *(5-0) = 1/2*5*5 = 12.5

1.3

The sales tax shifts the supply curve to the left . The new supply curve is denoted by S'.

1.4 The posted price for the good in the store is $5.

Consumers pay after giving sales tax = $5 + 10/100*5 = $5.50

Hence, the store collects = $ (5.50-5) = $5