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A linear demand function
(note linear means straight line- so you should always end up with one of these!)
This expresses the demand q (for example annual sales) as a linear function of the unit price p. It has the form
q = mp + b.
Note that m is always a negative due to the inverse relationship between price and quantity demanded.
Example The annual sales of your computer game "Braincraft" is given by
q = -40p + 8,000, (or it is often given q= 8000 - 40p..... it is the same thing.
where p is the price you charge per game. Thus, if you charge $35 per unit, you can expect to sell
q = -40(35) + 8,000 = 6,600
Prep:
HL Linear Demand Functions.docSummary notes:
With these questions you’ll always get a downward sloping line. If you don’t something has gone wrong
A typical function is:
Qd= X-aP eg Qd= 200- 5P
A change in X shifts the demand curve and a change in “a” will change the steepness of the slope.
More later on this.
Linear Supply Function,
A supply equation or supply function expresses q (the number of items suppliers are willing to make available) as a function of the unit price p (the price per item). A linear supply function has the form
q = mp + b
Here m is is a positive value and measures the change in supply per unit change in price. Thus for instance, if p is measured in dollars and q in monthly sales, and m = 400, then each $1 increase in the price per item will result in an increased supply of 400 items per month.
Another example
The number of T-shirts I am prepared to tie-dye and supply to Campus Creations Inc. per day depends on the price, $p, I obtain according to
q = 2.5p + 5.
For every $2 increase in price, I am willing to supply 5 additional shirts per day.
HL P3 Qs S and D .pdfEquilibrium Price
Demand and Supply are said to be in equilibrium when demand equals supply. The corresponding values of p and q are called the equilibrium price and equilibrium demand. To obtain the equilibrium price, set demand equal to supply and solve for the unit price p. To obtain the equilibrium demand, evaluate the demand (or supply) function at the equilibrium price.
HL Paper 3 sample question .doc
Now obviously if you are asked to fill in the gaps you do it. But if you just need to draw Supply and Demand Diagrams and work out equilibriums you can do it quicker simply by working out 2 points and joining and extending the lines.
Obviously P=0 is a good one to calculate but also calculate the equilibrium point as well just to check.
Changes in the linear functions
If for example Qd= a -bP
Then if "a" changes then this is a shift in the Demand curve (an increase in "a" is a shift to the right)
A change in "b" affects the steepness of the slope. The larger the value of "b" the shallower the demand curve is (the more "price elastic" demand is).
If for example Qs= c+dp
Then if "c" changes then this is a shift in the Supply curve (an increase in "a" is a shift to the right)
A change in "d" affects the steepness of the slope. The larger the value of "d" the shallower the supply curve is (the more "price elastic" supply is).
You have already seen in SL classes what consumer and producer surplus is. HL students also need to be able to calculate both of these mathematically.
A bit of basic maths:
The area of a triangle is 1/2 base x height.
So in the example above it looks like S cuts the P axis at zero (remember this isn't always so, so you may have to measure this in other examples). If D cuts the P axis at say 16, then half the base is 16-0/2=8. Now let's say the equilibrium Q is 2000. Then the total community surplus is8 x 2,000= 16,000$
You may also be asked to calculate both the producer and consumer surplus separately.
Student Task:
Using an appropriate diagram or equations, calculate the value of the consumer and producer surplus at the market equilibrium for a market defined by the following equations:
Qd=80-5P Qs=-24+8P
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