Linear+demand+functions

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: 

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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. <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 18px;">More later on this.

__**<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">Linear Supply Function, **__

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">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 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">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.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">q = mp + b

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">Another example <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;"> 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 <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">For every $2 increase in price, I am willing to supply 5 additional shirts per day.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">q = 2.5p + 5.

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<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">Equilibrium Price <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;"> 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.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">Demand: q = -4.5p + 4000 pairs per week
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">Supply: q = 50p - 1995 pairs per week

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<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">Short-cuts when working out these problems