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Derive and manipulate a straight line demand equation. Derive an equation for the total cost function(including volume-based discounts).
The straight line demand equation shows the relationship between price and demand.
Formula: Demand equation (P) = a – bQ
P = selling price
Q = Quantity demanded at that price
a = a theoretical maximum price at which there is no demand
b = the change in price required to change demand by 1 unit (gradient)
To calculate a:Formula: a = $(current price) + [ (current quantity at current price ÷ change in quantity when price is changed by $b) x $b]
To calculate b:
Formula: b = change in price ÷ change in quantity
For example
Our product is priced at $13. At this price, we sell 75 a month. When we raised the price to $15 we sold 50. Determine the demand equation.
P = a – bQ
a = $13 + [(75/25) x $2 = $19
b = (15 – 12) ÷ (75 – 50) = 0.12* Therefore P = 19 – 0.12Q
* 12 = 19 – 0.12 Q
* 12-19 = – 0.12 Q
* Q = 58.33
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