Question

Question 3: In a perfectly competitive market, the demand curve is given as: Q=100-4P, the supply curve is given as Q=2P-8. (20%) I. Compute the total social surplus. II. If the producers are now receiving a $4 per unit subsidy, graphically show the DWL of this market. III. Report the new social surplus with this subsidy. Question 4: In a market with demand: Q=200-2P, supply Q=P-40, if for every unit consumed, the society gets a benefit equivalent to $15 (MSB=$15) (25%) I. What is the SS when this is a free market? II. What is the DWL of the market due to the externality? III. Suppose the government uses a Pigouvian subsidy to correct this market failure, compute the CS, PS, S(subsidy), EB(external benefit) of the market under this tax.

Answer 1

The total social surplus in the perfectly competitive market is 294.

We need to get equilibrium price and quantity by setting the demand and supply equations equal to each other.

Q (demand) = 100 - 4P

Q (supply) = 2P - 8

Setting them equal:

100 - 4P = 2P - 8

100 + 8 = 2P + 4P

108 = 6P

P = 108 / 6

P = 18

So, the equilibrium price (P) is 18.

Using the demand equation:

Q = 100 - 4P where p is 18

Q = 100 - 4 * 18

Q = 100 - 72

Q = 28

The equilibrium quantity (Q) is 28.

Total social surplus:

= Consumer suplus + Producer surplus

= (1/2*(25-18)*28) + (1/2*(18-4)*28)

= 294

Answer 2

The total social surplus in the perfectly competitive market is 294.

We need to get equilibrium price and quantity by setting the demand and supply equations equal to each other.

Q (demand) = 100 - 4P

Q (supply) = 2P - 8

Setting them equal:

100 - 4P = 2P - 8

100 + 8 = 2P + 4P

108 = 6P

P = 108 / 6

P = 18

So, the equilibrium price (P) is 18.

Using the demand equation:

Q = 100 - 4P where p is 18

Q = 100 - 4 * 18

Q = 100 - 72

Q = 28

The equilibrium quantity (Q) is 28.

Total social surplus:

= Consumer suplus + Producer surplus

= (1/2*(25-18)*28) + (1/2*(18-4)*28)

= 294

Therefore, the total social surplus is 294.

ii. In the graph, the area b-c shows the dead-weight loss for giving $4 per unit subsidy on producer. It is attached below.