ECO/365 Version 4
Principles of Microeconomics
WEEK 1, DISCUSSION QUESTION 3
Suppose the demand and supply for milk are described by the following
equations: QD = 600 - 100P; QS = -150 + 150P, where P is price in dollars, Q D is
quantity demanded in millions of gallons per year, and Q S is quantity supplied in
millions of gallons per year.
1.
Use these equations to determine equilibrium price and quantity.
Now suppose the U.S. government imposes a $1 per gallon of milk tax on dairy
farmers.
1. Using the demand and supply equations from question 1: What is
the new equilibrium price and quantity?
1. How much do dairy farmers receive per gallon of milk after the tax?
How much do demanders pay?
2. Now suppose the tax is placed on the buyers of milk. Does it matter
who pays the tax?
5. Now, what is the new equilibrium price and quantity assuming the
government pays a subsidy of $1 per gallon (no tax now, just the subsidy)?
1. After the subsidy, how much do dairy farmers receive per gallon of
milk after the tax? How much do demanders pay?
For Discussion: what does this problem suggest to you about the impact of
government involvement in the supply and demand of specific products? How might
similar involvement impact your company?
Answer:
1.
Price
$1
2
Qd
Qs
500
400
0
150
3
300
300
4
200
450
5
100
600
You get these by plugging in each price ($1 to $5) in the two equations. Then
you can see that equilibrium price and quantity are at $3 and 300. Several of you put
in $300, which is a bit much to pay for a gallon of milk.
You can also solve without doing a table by setting the two equal to each other
and doing algebra:
600 - 100P = - 150 + 150P
750
3
=
=
250P
P
Then plug $3 into either equation for P and find out that Q = 300.
2.
The supplier now receives P - $1 so the supply equation becomes:
Qs = -150 + 150(P - 1), or Qs = -150 + 150P -150,
or Qs = - 300 + 150P.
This is the same as a leftward shift in the supply curve, also called a decrease in
supply. The demand curve does not change so to get the new equilibrium we do:
600 - 100P = - 300 + 150P
3.
900
= 250P
3.60
=
P
So the new price paid by the consumer is $3.60 which will give us a
quantity of 240. The supplier only gets to keep $2.60 since $1 is taken by the
government. Notice, the consumer pays 60 cents of the dollar (original price was $3
now its $3.60) and the supplier pays 40 cents (originally got $3 and now only gets
$2.60).
4.
The supplier will now have to pay an extra dollar to the government so
the new demand equation becomes:
Qd = 600 - 100(P + 1) or Qd = 600 - 100P -100 or Qd = 500 - 100P.
This is the same as a leftward shift in the demand curve, also called a decrease in
demand. The supply curve does not change so to get the new equilibrium we do:
500 - 100P = -150 + 150P (the original supply equation)
650
= 250P
2.60 = P
So, the price received by the supplier is again $2.60, while the consumer is again
paying $3.60 (P + $1), with the difference taken by the government (what the
government does with the money is for later chapters.) Notice, again, the consumer
pays 60 cents of the dollar (original price was $3 now its $3.60) and the supplier
pays 40 cents (originally got $3 and now only gets $2.60).
2 and 3 with a subsidy:
600 - 100P = - 150 + 150(P + 1)
600 - 100P = - 150 + 150P + 150
600
=
2.40 =
250P
P
The price falls to $2.40 but the Supplier gets $3.40. So, the subsidy benefits
consumers by 60 cents and the supplier by 40 cents.
Plugging in the price of $2.40 gives a quantity of 360.