Question

Consider the following market for board games: (Do NOT round values) ... can you please solve this on paper? Thank you!!

Qs= -20+4P Qd= 300-P

a) Calculate initial equilibrium supply and demand.

b) Calculate consumer and producer surplus. Show graphically.

c) Since board games make the world a better place, the government puts a $30 subsidy on all board games. Recalculate new equilibrium prices and quantity.

d) Show (c) in a graph and calculate consumer surplus, producer surplus, government cost and deadweight loss. Show these in the graph.

Answer 1

(a) In equilibrium, Qd = Qs

300 - P = - 20 + 4P

5P = 320

P = $64

Q = 300 - 64 = 236

(b)

From demand function,

When Qd = 0, P = $300 (Vertical intercept) & when P = 0, Qd = 300 (Horizontal intercept).

From supply function,

When Qs = 0, P = 20/4 = $5 (Vertical intercept).

Consumer surplus (CS) = Area between demand curve & price = (1/2) x $(300 - 64) x 236 = 118 x $236 = $27,848

Producer surplus (PS) = Area between supply curve & price = (1/2) x $(64 - 5) x 236 = 118 x $59 = $6,962

In following graph, AB and CD are demand and supply curves with above intercepts, intersecting at point X with price P0 (= $64) and quantity Q0 (= 236). CS equals area AXP0 and PS equals area CXP0.

(c) The subsidy will increase supply, shifting supply curve rightward. New supply function is

Qs = - 20 + 4(P + 30) = - 20 + 4P + 120 = 100 + 4P

Equating with Qd,

300 - P = 100 + 4P

5P = 200

P = $40

Q = 300 - 40 = 260

(d) From new supply function, when P = 0, Qs = 100 (Horizontal intercept).

In above graph, the subsidy shifts supply curve to EF, intersecting AB at point Y with price P1 (= $40) and quantity Q1 (= 260). Firms receive effect price of P2 (= P1 + $30 = $40 + $30 = $70). After subsidy, new CS is area AYP1 and new PS is area CZP2, cost to government is area P1YZP2 and deadweight loss equals area XYZ.

CS = (1/2) x $(300 - 40) x 260 = 130 x $260 = $33,800

PS = (1/2) x $(70 - 5) x 260 = 130 x $65 = $8,450

Cost to government = $30 x 260 = $7,800

Deadweight loss = (1/2) x $30 x (260 - 236) = $15 x 24 = $360