Question

d. What is the old and new PS and CS?

Answer 1

Solution:

Equilibrium occurs when quantity supplied and quantity demanded equal, and in case of without tax, the price paid by buyers also equals price received by sellers

So, 1.5 + 0.5*Q = 5.5 - 0.5*Q

Q* = 5.5 - 1.5 = 4 chocolate bars

And P* = 1.5 + 0.5*4 = $3.5 per chocolate bar

So, initial producer surplus, PS = (1/2)*(Q*)*(P* - 1.5)

PS = (1/2)*4*(3.5 - 1.5) = $4

Initial consumer surplus, CS = (1/2)*(Q*)*(5.5 - P*)

CS = (1/2)*4*(5.5 - 3.5) = $4

With tax, the equilibrium is found as follows:

Tax of $1 per chocolate bar creates a wedge of $1 between price paid by buyers, Pb, and received by sellers, Ps. In equilibrium, quantity demanded equals quantity supplied, however now Pb = Ps + 1

So, we have

Ps = 1.5 + 0.5*Q and

Ps + 1 = 5.5 - 0.5*Q or Ps = 4.5 - 0.5*Q

Thus, 1.5 + 0.5*Q = 4.5 - 0.5*Q

Q* = 4.5 - 1.5 = 3 chocolate bars

Ps = 1.5 + 0.5*3 = $3 per bar

Pb = 1 + Ps = 1 + 3 = $4 per bar

Thus, now the (new) producer surplus = (1/2)*(Q*)*(Ps - 1.5)

PS = (1/2)*3*(3 - 1.5) = $2.25

(New) Consumer surplus = (1/2)*(Q*)*(5.5 - Pb)

CS = (1/2)*3*(5.5 - 4) = $2.25