Question

5.1

Let market demand for solar panels be set by Q_d = 500-P and the industries supplies using
Qs =1/3P - 20. Draw a graph of the solar panel market and evaluate the equilibrium level of Q and P.
(a) Suppose the government offers a subsidy to producers of $48 per solar panel. Graphically represent this market-distortion.
(b) Numerically evaluate the quantity that clears the market (Q_sub), the price the consumer
pays (pc), and the price the producer receives (p_p).
(c) Graphically identify: Q_sub, p_c, p_p, the total cost of the subsidy to the government, the deadweight loss.
(d) Numerically evaluate the deadweight loss.

Answer 1

In equilibrium, Qd = Qs.

500 - P = (P/3) - 20

1500 - 3P = P - 60

4P = 1560

P = 390

Q = 500 - 390 = 110

(a)

After subsidy, supply will rise by $48 at every output level, shifting supply curve rightward. New supply function becomes

Qs = [(1/3) x (P + 48)] - 20

In following graph, D0 and S0 are pre-subsidy demand and supply curves intersecting at point A with price P0 (= 390) and quantity Q0 (= 110). After subsidy, S0 shifts right to S1, intersecting D0 at point B with price paid by buyers being Pc, price received by sellers being Pp and quantity being higher at Qsub.

(b)

Equating Qd and new Qs,

500 - P = [(1/3) x (P + 48)] - 20

1500 - 3P = P + 48 - 60

4P = 1512

P = 378 (Price paid by buyers = Pc)

Price received by sellers (Pp) = 378 + 48 = 426

Q (Qsub) = 500 - 378 = 122

(c)

In graph, Pc, Pp and Qsub are identified. Total cost to subsidy is area PcBCPp and Deadweight loss (DWL) is area ABC.

(d)

DWL = (1/2) x Unit subsidy x Change in Quantity = (1/2) x 48 x (122 - 110) = 24 x 12 = 288