IB Business & Management A Course Companion 2009 THE THEORY OF THE FIRM: COSTS, REVENUES AND PROFITS REVENUE THEORY IB Business & Management A Course Companion 2009

REVENUE THEORY Revenue is the income that a firm receives from selling its products, goods and services over a certain period of time Revenue may be measured in three ways: Total Revenue (TR) Average Revenue (AR) Marginal Revenue (MR)

Total Revenue (TR) TR is the total amount of money that a firm receives from selling a certain quantity of a good or service in a given time period. It is calculated using the formula: TR = p (the price of the good/service) x q (quantity) Example: If a firm sells 400 pizzas per week, at a price of $6 per pizza than TR = $2400.

Average Revenue (AR) AR is the revenue that a firm receives per unit of sales. It is calculated using the formula: AR + TR (Total Revenue p x q) q (Quantity) Since TR is (p x q), q is common to the top and bottom of the formula, so AR is the same as p. 400 pizzas at $6 each AR= $2400 / 400 = $6

Marginal Revenue (MR) MR is the extra revenue that a firm gains when it sells one more unit of a product in a given time period. It is calculated by using the formula: MR = __ TR___ where means “the change in” q

Marginal Revenue (MR) Example A pizza firms decides to lower the price of pizzas from $6 to $5. Weekly sales increased as follows: MR = $2500 – 2400 = $100 = $1 100 100 The extra revenue gain from selling an extra unit is $1

Revenue Curves and Outputs Revenue when price does not change with output (elasticity of demand = infinite) If a firm does not have to lower price as output increases and it wishes to sell more of its product, then if faces a perfectly elastic demand curve. This situation only happens in theory, but is very useful for economists when they are building their models of how markets work and they start with the theoretical market form of perfect competition.

REVENUE FOR A FIRM WITH A PERFECTLY ELASTIC DEMAND CURVE Assumptions The firm is very small in terms of the size of the whole industry and they can increase their output without affecting total industry supply, and thus price, in any significant way. Therefore the firm can sell all that it produces at the same price.

Total revenue increases at a constant rate as output increases. PRICE ELASTICITY OF DEMAND – INFINITE : REVENUE THEORY When the price elasticity of demand is perfectly elastic, the price, average revenue, marginal revenue and demand are all the same. In this case, they are all $5. Total revenue increases at a constant rate as output increases.

Revenue Curves and Outputs Revenue when price falls as output increase (when the demand curve is downward sloping i.e when elasticity of demand falls as output increases) If a firm wishes to sell more of its output and it can control the price at which it sells, then it will have to lower the price if it wants to increase demand.

If a firm wishes to sell more of its output and it can Revenue when price falls as output increases If a firm wishes to sell more of its output and it can control the price at which it sells, then it will have to lower the price if it wants to increase demand. The firm will face a downward sloping demand curve.

Output, revenue and PED figures for a firm with a normal demand curve

REVENUE THEORY Average revenue (AR) has obvious correlation with price and so it falls as output increases, since the price has to be lowered in order to sell more products. This is shown where demand curve is now labelled D=AR. Marginal Revenue (MR) also falls as output increases, but at a greater rate than AR. As shown in the graph the MR curve is twice as steeply sloping as the AR Curve and also goes below the x-axis. This is a relationship that holds for all downward sloping AR curves and the MR curves that relate to them.

Why is MR below AR in graphical analysis? MR is below AR because in order to sell more products, the firm has to lower the price of all products sold, losing revenue on the ones that could have been sold at a higher price in order to get the revenue from the extra sales.

Total Revenue in Graphical Analysis For a normal, downward-sloping demand curve, TR rises at first but will eventually start to fall as output increases. This is because the extra revenue gained from dropping the price and selling more units is outweighed by the loss in revenue from the units that were being sold at a higher price and now have to be sold at the lower price.

Relationship between the value of PED for a Demand Curve & TR The knowledge of the relationship between the value of PED for a demand curve and TR is very useful for firms when they are trying to assess the impact that a change in price of their product will have upon the total revenue they receive.

Inelastic Demand & Total Revenue If the firm raises prices and the demand is inelastic then the firm will find that total revenue will increase, because the increase in price will see a relatively smaller fall in the quantity demanded.

Elastic Demand and Total Revenue If the firm raises price and demand is elastic then the firm will find that total revenue will decrease, because the increase in price will cause a relatively larger fall in the quantity demanded. If a firm knows whether their demand is elastic or inelastic they know what pricing policy to adopt to increase their revenue.

ELASTICITY AND REVENUE POLICY When PED is elastic any firm wishing to increase revenue should lower its price. When PED is inelastic any firm wishing to increase revenue should increase its price. When PED is unity then any firm wishing to increase revenue should leave the price unchanged, since revenue is already maximised.

Draw a graph to graphically model this data. Clearly label all graphs.