Question

ECON 2110: PROBLEM SET 5 - CHAPTER 6 1. You live in Pawnee Indiana where the only suppliers of Soda are Paunch Burger restaurants. The following equations represent the demand and supply of sodas in Pawnee, where prices represent prices per soda and quantities are in 1000s of sodas. Qu=3-1p (a) What is the equilibrium Price andQuantity in this market? (b) Assume initially that there is no tax on the soda. What are the values of consumer surplus, producer surplus, total surplus, and dead weight loss in this market? ent was concerned about obesity in Pawnee and decided to impose a commodity tax (c) Suppose the govern on Paunch Burger Soda. If they wanted to reduce the quantity of sodas consumed to 1,000 sodas in all, What would be the appropriate soda tax amount? page 1 of 3 (d) If they implemented the soda tax proposed in part c, who would pay the majority of the tax, the buyers of the soda or Paunch Burger? What does this imply about the relative elasticities of supply and demand for soda in Pawnee? (e) If they Implemented the soda tax proposed in part c, what would be the values of consumer surplus, producer surplus, government revenue, total surplus (which incudes government revenue), and dead weight loss as a result of the tax? (compare these numbers to what you got in part b to make sure they make sense and seem correct). (f) If instead of a tax the government decided to give a subeidy of $1.50 per soda to Paunch Burger such that Paunch Burger received a total of $2.50 per soda and consumers only had to pay $1 per soda, how many sodas would be consumed? (g) Under the same circumstances as in part f. What would be the dead weight loss associated with such a subaidy? nage 2 of 3

Answer 1

Given:

QD 3 P 2. =

s=P S

(a) At equilibrium, we have

$Q_{D}=Q_{S}$

3 P P 2

-P 3 = 2

P=2

(Since quantity is given is thousands)

EQ=2000)

(b) We can represent the equations graphically as in the following diagram:

Price 6 Qs P CS 2 PS Qp 3-0.5P Quantity 0 2 3

Consumer Surplus (CS) is the area under the demand curve and above the equilibrium price. It is the Pink shaded area in the diagram given. We find the area of the pink triangle as:

CS Base Height 2.

CS (6 2) 2 4 2

Producer Surplus (PS) is the area under the equilibrium Price and above the supply curve. It is the area shaded in purple in the above diagram. We find the area of the Purple triangle to find the Producer surplus as:

$PS = \frac{1}{2}*Base*Height$

$\Rightarrow PS = \frac{1}{2}*2*2 = 2$

Dead weight loss is a loss in total surplus that occurs due to market inefficiencies. Here, the market is in equilibrium and the equilibrium values are calculated as usual. So, in this case, we have no dead weight loss (DWL).

$\Rightarrow DWL = 0$

Total Surplus is the sum of Producer surplus, Consumer surplus and DWL.

TS PS + CS =2 +4 = 6}

(c) A commodity tax is now applied to reduce the quantity of sodas consumed to 1000 units which results in a leftward shift of the demand curve. So we represent this graphically as:

Price 6 Qs P CS D Tax 3 2 P 1 PS Qp 3-0.5P Quantity 0 12 3 LO

$\Rightarrow Q_{D}=1$ (in thousands)

$\Rightarrow Q_{D}=3-\frac{1}{2}P_{D}$

$\Rightarrow 1=3-\frac{1}{2}P_{D}$

$\therefore P_{D} = 4$

Since Quantity bought and sold are the same and tax imposition implies different price being paid by the buyers and another price being received by the sellers, we have:

$\therefore Q_{D} = Q_{S} = 1$

$\therefore P_{S} = Q_{S} = 1$

The tax amount is the difference between the price paid by buyers and the price received by sellers.

$\therefore Tax = P_{D} - P_{S} = 4 - 1 = 3$

Therefore, the appropriate tax amount would be $3.

(d) The effect of tax can be shown graphically in the diagram below. The CS and PS are denoted in the same colours as before, tax in green and Dead weight loss in yellow.

The total tax amount is the yellow area.

$\therefore TaxTotal = 3*1 = 3$ (in thousands)

Tax paid borne by buyers and sellers are calculated below:

$\therefore Tax_{Buyers} =(4-2)*1 = 2$ (in thousands)

$\therefore Tax_{Sellers} =(2-1)*1 = 1$ (in thousands)

We thus see from the diagram as well as mathematically that Buyers would pay majority of the tax.

This implies that the demand for soda is more inelastic while the supply is relatively elastic to the demand. Here, supply is more elastic than demand which results in the burden of tax falling on the inelastic segment of the market, that is, the Buyers.

(e)

CS Base Height 2.

$\Rightarrow CS = \frac{1}{2}*(6-4)*1 = 1$

$PS = \frac{1}{2}*Base*Height$

$\Rightarrow PS = \frac{1}{2}*1*1 = 0.5$

Total Surplus after the imposition of tax is calculates as:

TSTar PS CS+GovRev 10.5+3 4.5

Since Dead Weight Loss is the loss in total surplus due to market inefficiencies, we can calculate DWL as the difference in Total Surplus before and after the tax is imposed.

$\Rightarrow DWL = TS - TS_{Tax} = 6 - 4.5 = 1.5$

This value of DWL is the same as the area of the Yellow region in the above diagram.