PowerPoint to accompany John Sloman Keith Norris

Lecture and Tutorial Purpose: To explain profit maximising conditions; Skills learning outcomes: - Students should be able to determine profit maximising output quantities; - Students should be able to calculate the profit at this level of output. This week – only up to the section titled some qualifications (Page 104). John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Chapter 5 Profit Maximisation

Build up a theory of Profit Maximisation What is the output and price where a firm maximises profits, How much profit does the firm make at that level? Total Profit = Total Revenue – Total Costs Tπ = TR – TC Similar to the cost breakdown there is: - Total Revenue, TR = P × Q - Average Revenue, P* = AR = TR / Q - Marginal Revenue, MR = TR / Q; *Exception is when there are different products in different markets then AR is the weighted average P John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Revenue Curves MR (Marginal Revenue is the extra total revenue gained by selling one more unit (per time period). So if a firm sells an extra 20 units this month compared with what it expected to sell and, in the process earns an extra $100, then it is getting an extra $5 for each extra unit sold: MR = $5. Revenue curves when price is not affected by the firm’s output (horizontal demand curve): Marginal Revenue (MR) = ∆TR / ∆Q = 100 / 20 = 5 How do the revenue concepts (i.e. TR, AR, MR vary with output; - Depends on market conditions for the particular firm; - Too small a firm cannot affect market prices & will have different looking revenue curves from a firm that is able to choose its own price. John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

i.e. accept the market determined equilibrium price; Revenue Curves when Price is not affected by the firm’s output (Fig. 5.1) If the firm is very small relative to the whole market, it is likely to be a price taker; i.e. accept the market determined equilibrium price; But being so small, it can sell as much as it is capable of producing at the price (Fig.5.1); Diagram (a) is the market (b) the firm; Firm demand is tiny relative to the whole market; Look at scale differences on the horizontal axis in the two diagrams; John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Deriving a Firm’s AR and MR: Price-taking Firm (fig. 5.1) AR, MR ($) Pe D O O Q (millions) Q (hundreds) (a) The market (b) The firm John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Deriving a Firm’s AR and MR: Price-taking Firm AR, MR ($) D = AR = MR Pe D O O Q (millions) Q (hundreds) (a) The market (b) The firm John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Deriving a Firm’s AR and MR: Price-taking Firm Market equilibrium price is $5 The firm is so small that any change in its output is too insignificant to affect the market price: - Therefore, the firm faces a horizontal demand ‘curve’ at this price; - It can sell 200 units, 600 units, 1200 units or whatever without affecting the $5 price; - Therefore, AR is a constant $5; - Therefore, the firm’s AR curve is equivalent to its straight line demand curve. John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Deriving a Firm’s AR and MR: Price-taking Firm With this horizontal demand curve, MR curve = AR curve; Since selling one or more unit at a constant price (AR) merely adds that amount to TR; If an extra unit is sold at a constant price of $5, an extra $5 is earned. Total Revenue (TR): As Price is constant, TR will increase at a constant rate as more is sold; The TR ‘curve’ will be a straight line through the origin. John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Total Revenue for a Price-taking Firm Quantity (units) Price = AR = MR ($) 200 400 600 800 1000 1200 5 TR ($) Q John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Total Revenue for a Price-taking Firm Quantity (units) Price = AR = MR ($) TR ($) 200 400 600 800 1000 1200 5 1000 2000 3000 4000 5000 6000 TR ($) Q John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Total Revenue for a Price-taking Firm TR Quantity (units) Price = AR = MR ($) TR ($) 200 400 600 800 1000 1200 5 1000 2000 3000 4000 5000 6000 TR ($) Q John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Revenue curves when the price varies with output Firm has a downward-sloping demand curve: - The firm has to lower the price to sell more; - If it raises its price it will sell less; - Average revenue (AR) = P; - P is reduced to sell ore then AR falls as output increases; - For price taking firm, the demand and AR curve are the same (Fig. 5.2) because AR = P; - The curve relating P to Q (i.e. demand curve) and AR to Q are the same curves (i.e. AR curves) John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Revenue curves when the price varies with output When a firm faces a downward sloping demand curve, MR is < AR & may be negative: - P must be lowered to sell more each time period; - Means lowering P for extra units plus the units it would have sold at the previous P; - Thus MR = PLUS – RFAD (table 5.1 & next diagram) where: PLUS = price of last unit sold, and RFAD = revenue lost in selling the other units at a lower price when it could have sold them at a higher price; John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

AR and MR Curves for a Firm Facing a Downward-sloping Demand Curve Q (units) P =AR ($) 1 2 3 4 5 6 7 8 7 6 5 4 3 2 AR, MR ($) AR Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

AR and MR Curves for a Firm Facing a Downward-sloping Demand Curve (Figure 5.2 p.100) Q (units) P =AR ($) TR ($) MR ($) 1 2 3 4 5 6 7 8 7 6 5 4 3 2 8 14 18 20 6 4 2 -2 -4 AR, MR ($) AR Quantity MR John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

AR and MR Curves for a Firm Facing a Downward-sloping Demand Curve MR is the extra revenue gained from selling one more unit; MR values are entered in the spaces between the figures for the other three columns (Table 5.1 and figure 5.2); When demand is price elastic: - A decrease in price will lead to a proportionately larger increase in Qd, hence - An increase in sales revenue (total consumer expenditure), - Therefore MR is positive / increasing ; When demand is price inelastic: - A decrease in price will lead to a proportionately smaller increase in Qd, hence - Therefore MR is negative / declining; If MR is a positive figure TR is increasing (i.e. sales per time are 4 units or less in figure 5.2): - The demand curve will be elastic at that quantity, If MR is negative and TR is falling (i.e. at a level of sales of 5 or more units in figure 5.2) the demand curve will be inelastic: - A rise in quantity sold would lead to a fall in TR. Thus, the D or AR curve in figure 5.2 is elastic to the left of point r and inelastic to its right. John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

TR Curve for a Firm Facing a Downward-sloping Demand Curve Quantity (units) 1 2 3 4 5 6 7 P = AR ($) 8 TR 14 18 20 TR ($) Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

TR Quantity (units) P = AR ($) TR ($) TR ($) 1 2 3 4 5 6 7 8 7 6 5 4 3 TR Curve for a Firm Facing a Downward-sloping Demand Curve – Figure 5.3 TR Quantity (units) P = AR ($) TR ($) TR ($) 1 2 3 4 5 6 7 8 7 6 5 4 3 2 8 14 18 20 Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

AR and MR Curves for a Firm Facing a Downward-sloping Demand Curve (Figure 5.2) Elastic Elasticity = -1 Inelastic AR, MR ($) AR Quantity MR John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

TR = P*Q (price times quantity, table 5.1); TR Curve for a Firm Facing a Downward-sloping Demand Curve – Table 5.1, Figure 5.3 Revenue TR = P*Q (price times quantity, table 5.1); TR starts to fall when MR is negative (where demand becomes inelastic); TR is maximum where MR = 0; At this point, Pєd = -1 John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

TR Elasticity = -1 Inelastic Elastic TR ($) Quantity TR Curve for a Firm Facing a Downward-sloping Demand Curve – Figure 5.3. Elasticity = -1 Elastic Inelastic TR TR ($) Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Shifts in revenue curves TR Curve for a Firm Facing a Downward-sloping Demand Curve – Figure 5.3. Shifts in revenue curves - A change in any other determinant of demand, such as tastes, income or the price of other goods, will shift the D curve; - By affecting the P at which each level of output can be sold, there will be a shift in all three revenue curves; - TR increase – vertical shift of TR curve upwards; - TR decrease – vertical shift of TR curve downwards; John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

5.2 Revenue, Costs and Profit What is the Short-run profit maximisation Output? Two ways to find this: - Maximise the difference between TR and TC using the TR and TC curves; - Use MR, AR, MC and AC curves (when comparing profit maximisation under different market conditions (Chapters 6 and 7); - Short run – at least one factor fixed; - Assume the firm is facing a downward sloping demand curve; John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Finding Maximum Profit Using Total Curves TR, TC, TP ($) Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Finding Maximum Profit Using Total Curves TR TR, TC, TP ($) Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Finding Maximum Profit Using Total Curves – Table 5.2 and Figure 5.4 TC TR TR, TC, TP ($) Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Finding Maximum Profit Using Total Curves TC TR TR, TC, TP ($) Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Finding Maximum Profit Using Total Curves TC TR TR, TC, TP ($) Quantity TP John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Finding Maximum Profit Using Total Curves TC b TR a TR, TC, TP ($) c d Quantity TP John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Finding Maximum Profit Using Total Curves TC d e TR TR, TC, TP ($) f Quantity TP John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

5.2 Revenue, Costs and Profit Using marginal and average curves – table 5.3 based on table 5.2 data: Stage 1: Profit is maximised at MR = MC (1) Produce table and draw curves – point e figure 5.5); (2) When Q < 3, MR > MC and therefore a larger addition to revenue than to costs so total profit will increase (as production increases); (3) When Q > 3, MC > MR and therefore a larger addition to costs than to revenue so total profit will decrease (as production increases); (4) If you cannot add anything more to a total, than the total is the maximum John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

5.2 Revenue, Costs and Profit Using marginal and average curves – table 5.3 based on table 5.2 data: Stage 2: Measuring profit size using AR and AC curves; (1) Data from table 5.3 is plotted in figure 5.6. (2) Calculate Average Profit: Aπ = AR – AC at the profit maximising output of 3; (3) Calculate Total Profit: Tπ = Aπ * Q (shaded area in figure 5.6) John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Finding the Profit-maximising Output Using Marginal Curves Costs and revenue ($) Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Finding the Profit-maximising Output Using Marginal Curves MC Costs and revenue ($) Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Finding the Profit-maximising Output Using Marginal Curves MC Costs and revenue ($) Profit-maximising output e Quantity MR John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Measuring the Maximum Profit Using Average Curves – Figure 5.6 MC Costs and revenue ($) Quantity MR John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Measuring the Maximum Profit Using Average Curves MC Costs and revenue ($) AR Quantity MR John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Measuring the Maximum Profit Using Average Curves MC Total profit = $1⅓ x 3 = $4.00 AC a Costs and revenue ($) 6.00 4⅔ Total Profit b AR Quantity MR John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

5.2 Revenue, Costs and Profit Some qualifications: Long-run profit maximisation Assuming that the AR and MR curves are the same in the long run as in the short run, LR profit maximisation is where MR = long run MC; The reasoning is the same as with the short-run case; the meaning of ‘profit’ loss minimising: still produce where MR = MC John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Loss-minimising Output MC AC Loss-minimising Output AR AC LOSS Q Costs and revenue ($) AR O Quantity MR John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Revenue, Costs and Profit Some qualifications long-run profit maximisation the meaning of ‘profit’ loss minimising: still produce where MR = MC short-run shut-down point: P = AVC John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

The Short-run Shut-down Point AC The Short-run Shut-down Point AVC AR P = AVC Costs and revenue ($) Q O Quantity John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Revenue, Costs and Profit Some qualifications: When AR and MR curves are the same in both short and long run long-run profit maximisation output is where MR = MC (long–run) the meaning of ‘profit’ One element of cost is the opportunity cost to the owners of the firm incurred by being in business; i.e. Minimum return that owners must make on capital to prevent them from eventually deciding to close down and undertake alternative activities; It is a cost because (like wages and rent) it has to be covered if the firm is to continue producing; Sometimes known as normal profit and is included in the cost curves John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Revenue, Costs and Profit Has two components: Normal Profit (%) = rate of interest on riskless loan + a risk premium: (1) Initial capital investment – the interest that could have been earned by lending the capital in some risk less form (i.e. a bank savings account): This defines the minimum rate of profit that entrepreneurs expect to earn. (2) Compensation for risk: - Varies according to business line; - Predictable patterns for food lines, relatively low: - Where outcomes are very uncertain (mineral exploration, fashion garment manufactures) relatively high. Thus earning normal profits means that owners will just be content to remain in that industry: - If they earn > normal profit => they will obviously prefer to stay in this business; - If they earn < normal profit => they will consider leaving and using their capital for another purpose. John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia

Revenue, Costs and Profit As Normal Profits are included in costs then any profits shown diagramatically must be over and above normal profit (figure 5.6): Known as Supernormal Profit, Pure Profit, Economic Profit, Abnormal Profit, Producer’s Surplus, or sometimes simply Profit; All mean excess of total profit over normal profit Loss Minimisation (at output where firm cannot make a profit) figure 5.7: - The AC curve is above the AR curve at all output levels; - Hence, the output at MR = MC is the loss-minimisation output; - The amount of loss (at MR = MC) is shown by the shaded area in figure 5.7 To produce or not to produce: - Fixed costs (rent and business rates) have to be paid even if we have zero (i.e. 0) output; - If the firm is covering more than its variable costs, it can go some way to paying off these fixed costs and therefore can continue to produce; - Short-run shut down point - It will shut down when it cannot cover variable costs (if AVC curve is above, or the AR curve is below (figure 5.8) - Long-run shut down point - If firm cannot cover LRAC (which includes normal profits) where the AR curve is tangential to LRAC curve. John Sloman, Keith Norris: Principles of Economics 2e © 2007 Pearson Education Australia