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3.3.1 Revenue

Revenue 


Total revenue - the income derived from sales of a product over a period of time. Often referred to as turnover. 

TR = P x Q

where Q is quantity sold and P is price sold at
Average revenue - revenue generated per unit of output sold. Found by dividing the TR by Q. 
It is the same as the demand curve. 

P = AR = TR/Q 

Marginal revenue - the revenue gained in selling an additional unit(s) of output. This is the rate of change of TR (so the gradient and the first differential). 

Image result for marginal revenue formula

Diagrammatic analysis 

Image result for revenue curve

As you can see here, MR is the gradient of TR - where the grad of TR is 0 (the maximum), MR cuts the x-axis. 

MR has a gradient that is double that of AR. 



Elasticity and revenue 


Image result for PED and revenue graph

Where demand is price elastic, a fall in price causes a greater than proportionate rise in demand, and revenue increases. Where price is elastic, the firm should price cut in order to increase revenue. 

Where demand is price inelastic, a rise in price causes a less than proportionate fall in demand, so revenue increases. When price is inelastic, the firm should increase prices in order to increase revenue. 

At unit elastic, the firm is revenue maximising - both increasing and decreasing the price would lead to a loss in revenue. So at the midpoint of the AR curve, or where MR = 0, the firm revenue maximises. 
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