Download Intro to Linear Functions (Supply, Demand) File

Demand, Supply, and Linear Functions (Micro 1.1)
(adapted from the Tragakes and Blink & Dorton textbooks)
Demand
A linear equation, called a demand function, can be used to show the relationship between the
demand for a product and individual determinants of demand. This is usually written in the form:
Qd = a – bP
where:
 Qd
= quantity demanded
 a
= the quantity that would be demanded if the price was zero (in other words, the xintercept)
 b
= slope of the demand curve.
 P
= price (the independent variable)
The demand function can be used to generate a demand schedule and then plot a demand curve.
For this demand function: QD = 500 – 10P



If the price were 0, the quantity demanded would be 500
If the price were 10, the quantity demanded would be 400
If the price were 20, the quantity demanded would be 300, and so on.
If the value of a were to increase, then:

the demand curve would shift to the right.
o Q: WHY?
 A: Remember the determinants!!!
o Q: Would this be a change in demand or a change in quantity demanded?
 A: This would be a change in demand b/c more would be demanded at a
given price,
If the value of b were to increase, then:

the demand curve would be flatter (more horizontal).
FYI: The greater the absolute value of
the slope, the flatter the curve.
o Q: WHY?
 People would have become more responsive to price changes (they are more
likely to change the quantity (amount) they purchase when the price changes)
o Q: Does this mean it becomes more elastic or more inelastic?
 More elastic.
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Supply
Similarly, a supply function can be used to show the relationship between the supply of a product
and individual determinants of supply. It is written in the form
Qs = c + dP
where:
 Qs
= quantity supplied
 c
= the quantity that would be supplied if the price was zero (in other words, the xintercept
 d
= slope of the supply curve.
 P
= price (the independent variable)
The supply function can be used to generate a supply schedule and then plot a supply curve.
For this supply function: Qs = -30 +20P




If the price were 0, the quantity supplied would be -30.
If the price were 1, the quantity supplied would be -10.
If the price were 2, the quantity supplied would be 10.
If the price were 3, the quantity supplied would be 30, and so on.
If the value of c were to increase, then:

the supply curve would shift to the right.
o Q: WHY?
 A: Remember the determinants!!!
o Q: Would this be a change in supply or a change in quantity supplied?
 A: This would be a change in supply b/c more would be supplied at a given
price.
o Q: Is this number almost always negative?
 A: Yes, because suppliers do not like to give away their product for free!
(However, a government subsidy could lead to supplying the product even if
the price is zero. WHY?!)
o Q: (Related to the previous Q) Should one draw a supply curve with either a negative
price or a negative quanity?
 A: No! For the above example, start drawing the supply curve @ the price of
1.5 and the quantity of zero.
If the value of d were to increase, then:

the supply curve would become flatter (more horizontal). REMINDER: The greater the
absolute value of the slope, the flatter the curve.
o Q: WHY?
 A: People would have become more responsive to price changes (they are
more likely to change the quantity (amount) they purchase when the price
changes)
o Q: Does this mean it becomes more elastic or inelastic?
 A: elastic.
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VISUALIZING THE DEMAND & SUPPLY FUNCTIONS
(diagrams from Tragakes)
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Equilibrium
Equilibrium is the price where the supply and demand curve intersects.
Without using graphing, it is possible to calculate the equilibrium price and equilibrium
quantity from linear demand and supply functions. This can be done by solving simultaneous
linear equations.
The key thing to remember is, at market equilibrium:
Qd = Qs
One example:
 Part I: The Original Info
o Qd = 1400 – 200P
o Qs = -400 + 400P
o (Reminder: Qd = Qs)
 Part II: Discovering the Equilibrium Price
o 1400 – 200P = -400 + 400P
o 1800 = 600P
o 3=P
 Part III: Discovering the Equilibrium Quantity Demanded & Supplied
o Qd = 1400 – 200(3)
 1400-600
 800
o Qs = -400 +400(3)
 -400+1200
 800
o 800 = 800
For any price other than the equilibrium price, there will either be excess demand (a
shortage) or excess supply (a surplus).
 If there is no government intervention, then the amount supplied or demanded
will naturally adjust until a new equilibrium is reached.
 If there is a price ceiling or a price floor, then a new equilibrium is not reached.
To calculate the excess supply or demand at a given price, enter in a price and
compare the quantity supplied to the quantity demanded. Here is an example using
the same original numbers as above but setting the price at 5 instead of 3 (equil.):
o Qd = 1400 – 200P
 1400-1000
 400
o Qs = -400 + 400P
 -400 + 2000  1600
o ***At the price of 5, there is an excess supply (surplus) of 1200.***
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Linear Demand, Supply, & Equilibrium Practice
1. Write the equation for linear demand and identify each part. Why does b have a
negative sign?
2. Write the equation for linear supply and identify each part. Why is c often negative?
For questions #3-6, here are the demand and supply functions:
Market for photo frames
Qd = 900 – 100P
Qs = -300 + 200P
3. Make a demand and supply schedule for photo frames at the following prices: $0, $1,
$2, $3, $4, $5, and $6.
4. Using simultaneous equations, calculate the equilibrium price and equilibrium
quantity from linear demand and supply functions. (Use equations…don’t diagram!)
5. At the price of $3, is there an excess supply or an excess demand? By how much?
6. Draw a diagram that demonstrates demand, supply, and the equilibrium price. On the
same diagram, indicate the excess supply or excess demand at the price of $3.
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For questions #7-11, here are the demand and supply functions:
Market for widgets (FYI: P is in € and Q is in million units per month)
Qd = 27 – .7P
Qs = -5 + .9P
7. Calculate the equilibrium price and quantity.
8. Plot the demand & supply functions and identify the equilibrium P & Q on the graph.
9. When P = €25, is there excess demand or supply? By how much?
10. (No need to diagram for this Q) Assume that the slope of the demand function falls to
-0.9. (a) State the new demand function. (b) What happens to the steepness of the
demand curve? (c) Does the demand for widgets become more elastic or inelastic?
(d) Why?
11. (No need to diagram for this Q) Assume the slope of the supply function rises to 1.6. (a)
State the new supply function. (b) What happens to the steepness of the demand
curve? (c) Does the demand for widgets become more elastic or inelastic? (d) Why?
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