Question

4. The handmade snuffbox industry is composed of 100 identical firms, each having short- run total costs given by S by SMC-q+10 where q is the output of snuffboxes per day a) What is the short-run supply curve for each snuffbox maker? What is the short-run supply curve for the market as a whole? b) Suppose the demand for total snuffbox production is given by Q 1100-50P What is the equilibrium in this marketplace? What is each firm's total short-run profit? Graph the market equilibrium and compute total producer surplus in this case Suppose now the government imposed a S3 tax on snuffbox. How would this tax change the market equilibrium? c) d) e) How would the burden of this tax be shared between snuffbox buyers and sellers? f) Calculate the total loss of producer surplus as a result of taxation of snuffbox g) Calculate the deadweight loss if $3 tax is imposed.

Just need D, E, F and G answered.

Answer 1

(d) The $3 tax will shift supply curve leftward by $3 at every output level. New supply function becomes

P - 3 = q + 10

P = q + 13

With 100 firms, Qs = 100q, so q = Qs/100

P = (Qs/100) + 13

Qs/100 = P - 13

Qs = 100P - 1300 (new supply curve)

Equating with Qd,

1100 - 50P = 100P - 1300

150P = 2400

P = 16

Q = (100 x 16) - 1300 = 1600 - 1300 = 300

q = 300/100 = 3

Therefore, market price increases by 2 (= 16 - 14), market quantity decreases by 100 (= 400 - 300) and firm output decreases by 1 (= 4 - 3).

(e)

Price paid by buyers after tax = 16

Tax borne by buyers = After-tax price paid - Pre-tax price = 16 - 14 = 2

Price received by sellers after tax = 16 - 3 = 13

Tax borne by sellers = Pre-tax price - After-tax price received = 14 - 13 = 1

(f)

From pre-tax supply function, when Q = 0, P = 1000/100 = 10 (Minimum acceptable price)

Producer surplus (PS) = Area between supply curve and market price = (1/2) x (14 - 10) x 400 = 200 x 4 = 800

After tax, PS = (1/2) x (13 - 10) x 300 = 150 x 3 = 450

Loss in PS = 800 - 450 = 350

(g)

Deadweight loss = (1/2) x Change in market price x Change in market quantity = (1/2) x (16 - 14) x (400 - 300)

= (1/2) x 2 x 100 = 100