Question

The following equations represent the inverse supply and demand functions in the market for Good A: PC = 80 - ½ QD PP = 14 + QS where PC and PP are the prices paid by consumers and received by producers respectively. QD and QS are the quantities demanded and supplied, respectively.

c) (2pts) Compute the competitive market equilibrium price and output with the tax.
d) (4pts) Compute producer surplus and consumer surplus with the tax.e the government is considering imposing a tax of $6 per unit of Good A.

Answer 1

The price paid by the consumers comes from the demand function.

The price received by the producers comes from the supply function.

Hence,

The demand function is:

Pe= 80 – Qd

The supply function is:

P = 14+Q5

Price Price paid by buyer 1 A Deadweight loss Supply Tax Price received by seller Demand + + + + + + + + + + + + Quantity Quantity traded

Here, the tax imposed by the government = 6 per unit of the good (this is marked as "tax" in the diagram above)

Part c:

We know that the tax = 6.

At equilibrium,

Pc-Pp = tar

Hence,

(80 --Qa) – (14 + Qs) = tax = 6

Also, at equilibrium, Qs = Qd

Let this quantity at equilibrium be equal to Q*

Therefore,

(80 –Q*) – (14+Q*) = tax = 6

Solving, we get:

Q* = 40

The corresponding values of Pc and Pp at equilibrium are:

Pe= 80 - -Q*

P,= 14 + Q* = 14 + 40 = 54

Part d:

and producer The wonsumer Surplus after of tax is given by the introduction cs = ps = ane a area of A F [the triangle A in diagram]

P. - 14+ - 54 * 40 hy found in preniosis pont. The intercepts of the demand and supply curne com be found by making &=0. a when so = o p = 80-0=80 = ₂ When as=0 - 14+0= 14= 4 » G = 14 g = 80

ara A = I x (62 - P*) x 8 * - 1 x (80 - 600 x 40 = 20% 20 = 400 = CS area F = I x (Pt. 4) x Qa = I x (54-14) x8* = fx 40 x 40 = 800-PS

Thus,

CS = 400

PS = 800