Question

It considers that the following equations represent the supply and demand of honey in the national market. Answer the following questions: ?? = 400−2? ?? = 12?

a. Find the market balance.

b. Calculate the consumer and producer surplus.

c. Suppose the government wants to encourage honey consumption for more bees. For the above, the government decides to give a subsidy of a tax of 10 pesos is applied for each unit sold of honey, calculates the new market amount. Tip: Remember the equilibrium condition of the supply and demand model and proceed in a very similar way as if it were a tax, only that consumers will now pay a lower price.

d. Is the amount of subsidy paid by the Government greater or less than increases in consumer surplus? What would you call this difference?

Answer 1

(a)

When the market balances, Qd = Qs.

400 - 2P = 12P

14P = 400

P = 28.57

Q = 12 x 28.57 = 342.84

(b)

From demand function, when Qd = 0, P = 400/2 = 200 (Vertical intercept of demand curve).

Consumer surplus (CS) = Area between demand curve & price = (1/2) x (200 - 28.57) x 342.84 = 171.42 x 171.43

= 29,386.53

From supply function, when Qd = 0, P = 0 (Vertical intercept of supply curve).

Producer surplus (PS) = Area between supply curve & price = (1/2) x (28.57 - 0) x 342.84 = 171.42 x 28.57

= 4,897.47

(c)

Subsidy will increase effective price received by sellers, shifting supply curve rightward by $10 per unit. New supply function:

Qs = 12(P + 10)

Qs = 12P + 120

Equating with Qd,

400 - 2P = 12P + 120

14P = 280

P = 20 (Price paid by buyers)

Price received by sellers = 20 + 10 = 30

Q = 400 - (2 x 20) = 400 - 40 = 360

(d)

Cost of subsidy to government = Subsidy per unit x Quantity after subsidy = 10 x 360 = 3,600

New CS = (1/2) x (200 - 20) x 360 = 180 x 180 = 32,400

Increase in CS = 32,400 - 29,386.53 = 3,013.47

Therefore,

Cost of subsidy to government > Increase in CS.

This difference is called social inefficiency (deadweight loss).