Question

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Suppose the demand for and supply of ethanol in a small town are as follow:

Qd = 9,000 - 1,000P
Qs = 2,000P - 3,000

● Where Q measures gallons per day and P represents price per gallon. The current equilibrium price $4, and the current equilibrium quantity is 5,000 gallons per day.
● Now suppose that the government wants to create a subsidy of $0.375 per gallon to encourage the use of ethanol.

a. What will happen to the price buyers pay per gallon, the price sellers receive per gallon, and the number of gallons consumed each day?
b. How much will this subsidy cost the government?

Answer 1

Solution: We are given the following equations of demand and supply of ethanol.

Firstly, we will try calculating the equilibrium price and quantity of ethanol from the following two equations.

To estimate equilibrium, we have to equate both the demand and supply.

That is, Demand = Supply

This imply, Qd=Qs

9,000-1,000P = 2,000P-3,000

9,000+3,000=2.000P+1,000P

12,000=3,000P

$4=P

Hence equilibrium price is $4.

So we can substitute the value of P in demand equation (or supply equation) to estimate the equilibrium quantity.

Let’s do it by putting in demand equation.

Q=9,000-1,000P

Q=9,000-1,000*(4)

Q=9,000-4,000=5,000

Hence equilibrium quantity is 5,000 units.

Now suppose that the government wants to create a subsidy of $0.375 per gallon to encourage the use of ethanol.

1. What will happen to the price buyers pay per gallon, the price sellers receive per gallon, and the number of gallons consumed each day?

A subsidy is a certain amount of money, usually given by a government entity, to help a business or an industry keep prices for its goods or services competitive or low enough to remain affordable.

When subsidies are introduced, it will help the producers to bring down their costs and supply more quantities in the market. With this, the producer’s supply curve will shift to the right and this will lead to increase in quantity supplied and a fall in the price.

There will be a change in the supply equation.

Earlier Q=2,000P-3,000

From here we can estimate the price,

Q+3,000=2,000P

This imply, (Q+3,000)/2,000=P

Now the price has lower down by the amount of subsidy

(Q+3,000)/2,000-0375=P

(Q+3,000-750)/2,000=P……………..by taking l.c.m

(Q+2,250)/2,000=P

Also we will change the demand equation in terms of P

Q=9,000-1,000P

1,000P=9,000-Q

This imply P= (9,000-Q)/1,000

Now we will equate both new equations of demand and supply.

Qd=Qs

(9,000-Q)/1,000 = (Q+2,250)/2,000

On solving we get

18,000-2Q = Q+2,250

18,000-2,250 = Q+2Q

15,750 = 3Q

15,750/3 = Q

5,250 = Q

So the equilibrium quantity supplied will rise from 5,000 to 5,250 units

Equilibrium price will become = P = (9,000-5,250)/1,000

P = $3.75

The equilibrium price will fall from $4 to $3.75

Therefore the price that will be borne by the consumer is $3.75, which is the equilibrium price

The producer will receive a higher price because of the effect of subsidy.

We can estimate the price receive by the producer by using the supply equation and using the new equilibrium quantity.

Qs = 2,000P-3,000

Therefore P = (Qs+3,000)/2,000

P = (5,250+3,000)/2,000

P = 8,250/2,000

P = $4.125

So producer will receive the price of $4.125

How much will this subsidy cost the government?

We can calculate the cost of subsidy by multiplying the amount supplied and the subsidy price that is,

Subsidy = $0.375*5,250

             = $1,968.75