Question

1. Consider a free market with demand equal to Qd = 900 – 10P and supply equal to Qs = 20P.

   1. What is the value of consumer surplus (CS) when the market is in equilibrium? What is the value of producer surplus (PS) when the market is in equilibrium?

   2. Graph the supply and demand curves and identify the equilibrium price and quantity on your graph. Show CS and PS on your graph of the demand and supply curves.

   3. Now suppose the government imposes a $15 per unit subsidy on the production of the good. What is the consumer surplus now? The producer surplus? Why is there deadweight loss associated with the subsidy, and what is the size of this loss?

   4. Explain in your own words what deadweight loss is and why it is relevant in the study of public sector economics.

Answer 1

a) At the equilibrium we have

Qd = Qs

900 – 10P = 20P

900 = 30P

P = 900/30

P = $30 per unit

Q = 900 – 10*30 = 600 units

CS = 0.5*(maximum price – price buyers pay)*qty purchased = 0.5*(900/10 – 30)*600 = $18000

PS = 0.5*(price sellers receive – minimum price)*qty sold = 0.5*(30 – 0)*600 = $9000

b) After the subsidy is provided, the market supply is Qs = 20(P + 15) or Qs = 300 + 20P.

New market equilibrium price is

Qd = Qs

900 – 10P = 300 + 20P

P = 600/30 = $20 per unit (price paid by buyers)

Market quantity Q = 900 – 10*20 = 700 units

Price received by sellers is 20 + 15 = $35 per unit

CS = 0.5*(maximum price – price buyers pay)*qty purchased = 0.5*(900/10 – 20)*700 = $24500

PS = 0.5*(price sellers receive – minimum price)*qty sold = 0.5*(35 – 0)*700 = $12250

Size of DWL = 0.5*subsidy*increase in qty = 0.5*15*100 = $750

DWL is an efficiency loss resulting from inefficient production. It composes of consumption and production distortionary losses. A tax or a subsidy create a wedge between prices that buyers and sellers are engaged with and thus, prevent market from reaching an equilibrium.

In this case government bears a greater cost of subsidy than the rise in consumer and producer surplus and due to this reason there is a deadweight loss.