4. In the market for ballet shoes, the demand curve is Q^D=300-3P and the supply curve is Q = P. The government imposes a tax on producers of 20. What is the price paid by buyers after the tax? What is the price received by sellers after the tax? Depict the following solution

graphically:

Answer: p^B=80,P^S=60

Inverse Demand function: solve the demand function for P.

P=100-1/3Q^D

Inverse supply function

P=Q^S

Set demand equal to supply and solve for P.

300-3P=P

P=300/4=75

Equilibrium Price before taxes.

Q=300-3*75=75=75

New inverse supply curve.

S':P=Q^S+20

Tax reduces the supply of ballet shoes.

S':Q^S=-20+ P

Resolve for P with the new inverse supply curve.

300-3P=-20+P

P=320/4 =80

Price paid by buyers after the tax.

P^B = 80

Plug the the price that the buyers pay into the tax adjusted inverse supply curve.

Q^S = -20+80

Recall that the inverse supply curve is equal to price.P=Q^S=60

The price sellers receive after the tax.

P^S = 60

To find the price paid by buyers after the tax, we need to calculate the new equilibrium price using the new supply curve. We can do this by setting the demand equal to the supply and solving for P.

300 - 3P = P

Simplifying the equation, we get:

4P = 300

P = 75

So, the equilibrium price before the tax is $75.

Now, we need to calculate the new equilibrium price after the tax. The new supply curve is given by:

S': P = Q^S + 20

Substituting the equilibrium price before the tax, we get:

S': P = 75 + 20

Simplifying the equation, we get:

P = 95

So, the new equilibrium price after the tax is $95.

The price paid by buyers after the tax is the same as the equilibrium price after the tax, which is $95.

The price received by sellers after the tax is the equilibrium price after the tax minus the tax amount, which is $95 - $20 = $75.

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