Question

3- In a perfectly competitive market the demand and supply functions for a product is given by
?? = 200 − 4?
?? = −100 + 6?
Now suppose that the government taxes the good by a unit tax of 5TL.
a) Find the price that demanders pay and the price that suppliers receive when buyers are
responsible to pay for the tax. Find the total tax collection and the deadweight loss from
this taxation policy. Show your analysis explicitly on a graph. (15 Pts)
b) Find the price that demanders pay and the price that suppliers receive when sellers are
responsible to pay for the tax. Find the total tax collection and the deadweight loss from
this taxation policy. Show your analysis explicitly on a graph. (15 Pts)

Answer 1

Based on the equations given,

Y-Intercept of demand curve is 50 (when Qd = 0)

Y-Intercept of supply curve is 16.67 (when Qs = 0)

Equating demand and supply,

Qd = Qs

200 - 4p = (-100) + 6p

300 = 10p

p = 30TL

Q = 80

Before tax, equilibrium price is 30TL, and quantity is 80 units.

Now, regardless of whether a tax is imposed on the buyer or the seller, the tax incidence depends on elasticity. Thus, the outcome remains the same.

a) When tax is imposed on buyer, the demand curve shifts to the left:

First, Qd = 200 - 4p and thus, p = 50 - Qd/4

Adding the tax of 5TL to demand curve

p + 5 = 50 - Qd/4

p = 45 - Qd/4

Qs = -100 + 6p

Q = -100 + 6(45 - Q/4)

Q = -100 + 270 - 3/2Q

5/2Q = 170

Q = 68

Ps = 28TL

Pb = 33TL

After tax, price that sellers receive is 28TL, and price that buyers pay is 33TL. Quantity reduces to 68 units.

In the diagram, the pink rectangle is tax collection. The blue triangle is deadweight loss.

Area of rectangle = 68 x 5 = 340TL     ----   tax collection

Area of triangle = 1/2 x 5 x 12 = 30TL     ----     deadweight loss

b) When tax is imposed on seller, the supply curve shifts to the left:

Qd = 200 - 4p

Qs = -100 + 6p

Therefore, p = (Q + 100) / 6

Adding the tax of 5TL to supply curve

p + 5 = Q/6 + 100/6

p = Q/6 + 100/6 - 5

Q = 200 - 4(Q/6 + 100/6 - 5)

Q = 200 - 2/3Q - 400/6 - 20

5/3Q = 180 - 400/6

5Q = 540 - 1200/6

5Q = 540 - 200

5Q = 340

Q = 68

Ps = 28TL

Pb = 33TL

After tax, price that sellers receive is 28TL, and price that buyers pay is 33TL. Quantity reduces to 68 units.

In the diagram, the pink rectangle is tax collection. The blue triangle is deadweight loss.

Area of rectangle = 68 x 5 = 340TL     ----   tax collection

Area of triangle = 1/2 x 5 x 12 = 30TL     ----     deadweight loss

Conclusion

A tax on buyers shifts the demand curve to the left. A tax on sellers shifts the supply curve to the left.

The net outcome of tax incidence remains the same in either case, and it depends on elasticity of demand and supply.

Due to the tax, the buyers end up paying more, and sellers end up receiving less, than earlier. The difference goes to the government as tax revenue. As the equilibrium is disturbed, it leads to deadweight loss.