Question

Q d= 20- 2P

Qs = 4p -10

1. Derive equilibrium price and quantity for this market.
2. Calculate Ed,p and Es, p at the above equilibrium
3. If a one dollar excise tax is imposed on buyers, what will be the tax burden shouldered by buyers and sellers respectively?
4. Show the price paid by buyers and received by sellers respectively.
5. Calculate DWL due to this tax.
6. Given the same demand and supply, if a one-dollar subsidy is provided to the sellers, what will be the price paid by consumers and received by sellers respectively?
7. What will be the total cost of this subsidy paid by the government?
8. Calculate DWL under subsidy.

Answer 1

(1)

In equilibrium, Qd = Qs.

20 - 2P = 4P - 10

6P = 30

P = $5

Q = 20 - (2 x 5) = 20 - 10 = 10

(2)

Ed = (dQd/dP) x (P/Qd) = -2 x (5/10) = -1

Es = (dQs/dP) x (P/Qs) = 4 x (5/10) = 2

(3)

Tax burden of buyers = Es / (Ed** + Es) = 2 / (1 + 2) = 2 / 3 = 0.67 = $1 x 0.67 = $0.67

Tax burden of sellers = Ed** / (Ed** + Es) = 1 / (1 + 2) = 1 / 3 = 0.33 = $1 x 0.33 = $0.33

**Absolute value of elasticity of demand is considered.

(4)

The $1 tax will increase effective price paid by buyers, which will decrease demand. New demand function will be

Qd = 20 - 2(P + 1) = 20 - 2P - 2 = 18 - 2P

Equating with Qs,

18 - 2P = 4P - 10

6P = 28

P = $4.67 (Price received by sellers)

Price paid by buyers = $4.67 + $1 = $5.67

Q = (4 x 4.67) - 10 = 18.68 - 10 = 8.68

(5)

DWL = (1/2) x Unit tax x Change in quantity = (1/2) x $1 x (10 - 8.68) = $0.5 x 1.32 = $0.66

NOTE: As per Answering Policy, 1st 5 parts are answered.