Answer to Question #160041 in Microeconomics for Bukola

Question

Calculate the market for ponche an alcoholic wine.the demand is characterized by the following equation p_d=100-Q_d.the supply is given by P_s=0.25Q_s

a.Determine the equilibrium quantity and price

b.suppose an ad valorem tax of 100% is imposed on buyers of the wine ,graphically sketch the behaviour of the demand and supply curve.

c.what is the new equilibrium price and quantity?

what are the price that buyers will pay and suppliers will get? Also determine the tax revenue and tax incidence on the buyers and seller

Answer 1

a) Let's find the initial equilibrium (equilibrium price and quantity). In the equilibrium, $P_d=P_s$ and $Q_d=Q_s$, so we can find the equilibrium quantity:

$$100-Q_E=0.25Q_E,$$ $$Q_E=80.$$

Then, we can find the equilibrium price by substituting $Q_E$ into the equation for $P_d$:

$$P_E=100-Q_E=100-80=\$20.$$

b)-c) Let's rewrite our demand and supply functions as follows:

$$Q_d=100-P_d,$$ $$Q_s=4P_s.$$

Now, an ad valorem tax of 100% is imposed on buyers of the wine. Therefore, for supply function we get:

$$Q_s=4P_s-P_s=3P_s.$$

Finally, we can calculate the new equilibrium price and equilibrium quantity:

$$3P_{Enew}=100-P_{Enew},$$ $$P_{Enew}=\$25.$$ $$Q_{Enew}=100-25=75.$$

Let's plot the demand and supply curves in Excel:

Here, orange line is the supply function, the blue curve is the demand function and the gray curve is the new supply function after the taxation.

The tax revenue can be calculated as follows:

$$Tax\ Revenue=(P_{new}-Pp)Q_{new},$$

here, $P_{new}=\$25$ is new equilibrium price after taxation, $Pp=\$18.75$ price per unit received by sellers (or producers) after taxation, $Q_{new}=75$ is the new equilibrium quantity.

Then, we get:

$$Tax\ Revenue=(\$25-\$18.75)\cdot75=\$468.75.$$

Let's also calculate buyers and sellers tax incidence.

Buyers tax incidence is given by the difference between the price paid $P_{new}$ and the initial equilibrium price $P_e$ multiplied by $Q_{new}$:

$Buyers\ Tax\ Incidence=(P_{new}-P_e)Q_{new}=(\$25-\$20)\cdot75=\$375.$

Sellers tax incidence is given by the difference between the initial equilibrium price $P_e$ and the price they receive after the tax is introduced $P_p$ multiplied by $Q_{new}$:

$Sellers\ Tax\ Incidence=(P_e-P_p)Q_{new}=(\$20-\$18.75)\cdot75=\$93.75$