Answer to Question #152648 in Microeconomics for Nga

Question

Domestic supply Qs= P-50 and demand Qd= -P+100. World price = 50. Determine the change in consumer and producer surplus, net gain. What amount of subsidies should the state provide to the producer in order to completely exclude imports.

Answer 1

ANSWER

1. The change in consumer and producer surplus

Consumer surplus is the gain obtained by consumers due to a difference between highest price that they are willing to pay (according to the demand curve) and the market price that they can pay.

Let's assume that an initial market state is the market equilibruim. According to this assumption we can find the market (equilibrium) quantity and the market (equilibrium) price using the following equation

Qd(Pe)=Qs(Pe), where Pe - is the equilibrium price

Hence,

$Pe-50=-Pe+100$

Hence, 2Pe=150. Hence, Pe = 75.

The equilibrium price allows to calculate the equilibrium quantity using the function Qd or Qs.

The equilibrium quantity (Qe) is 25 ( 75 - 50 or -75+100).

Consumer surplus can be calculated as the definite integral of the demand function with respect to price, from the market price (Pe) to the maximum price. This maximum price is the price of product when the Qd is equal to zero. Hence, the maximum price is 100 (Qd = 0 = -P + 100, hence P=100 is the maximum price).

The indefinite integral of the demand function with respect to price can be calculated as follows:

$\int$$Qd(P)dp=\int(-P+100)dP=C+100P-P^2/2$

Using the last formula we can find the consumer surplus:

$C+100*100-100^2/2-C-100*75+75^2/2=2,500-2,187.5=312.5$

Producer surplus can be calculated as the definite integral of the supply function with respect to price, from the minimum price to market price (Pe). This minimum price is the price of product when the Qs is equal to zero. Hence, the minimum price is 50 (Qs = 0 = P - 50, hence P=50 is the minimum price).

The indefinite integral of the supply function with respect to price can be calculated as follows:

$\int Qs(P)dP=\int (P-50)dP=C-50P+P^2/2$

Using the last formula we can find the producer surplus:

$C-50*75+75^2/2-C+50*50-50^2/2=312.5$

The world price can change the initial consumer surplus and producer surplus. The changes are depicted in the surpluse diagram (attached to the answer).

The geometrical analyses shows that the consumer surplus was doubled. The producer's surplus was decreased. The producer's surplus is zero when the world price is 50.

2. Amount of subsidies

To exclude import the amount of subsidies should be caalculated as difference between equilibruim price and world price or 25 = 75 - 50 (if the amount of subsidies is equal to zero, the producer's loss = - 25 per unit). The amount of subsudies that is equal to 25 allows to achieve the world price without any changes in supplier's profit and hence its supply curve.