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Mastering Price Elasticity: Maximizing Total Revenue

Learn how to optimize revenue through price elasticity of demand. Understand the relationship between price, quantity, and revenue to make strategic pricing decisions. Solve puzzles and calculate profits with practical examples.

lisandra-chambers
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Mastering Price Elasticity: Maximizing Total Revenue

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  1. The Mantra: MR = MC Total Revenue = Price x Quantity TR = Px Change in Total Revenue = TR TR = P x + x P TR = Output Effect + Price Effect Output effect: sell more at same price as before … but to sell more Price effect: must lower price on all the units you’re already selling

  2. Price Elasticity of Demand (=E) • E = Percentage increase in quantity demanded in response to a 1% decrease in price E = - (Δx/x) ÷ (ΔP/P) • We define price elasticity of demand, E, to be positive • When price rises, quantity demanded falls  (Δx/x) ÷ (ΔP/P) is always negative • Since E = - (Δx/x) ÷ (ΔP/P), we speak of demand elasticity as a positive number.

  3. Price Elasticity and MR TR = Px TR = P x + x P MR = TR/x = P + (x/x) P = P [1 + (x/x) (P/P)] = P [1+ (P/P) ÷ (x/x)] MR =P [1 - 1/E] where E = - (x/x) ÷ (P/P), i.e., E is a positive number. E > 1, x up a lot when P down a little TR up E < 1, x up a little when P down a lot TR down

  4. Puzzle 1: Luxury Boxes MC = $ 300,000 P = $1,000,000 when x = 25 Sell More Boxes ???

  5. Puzzle 2: Soccer Seats Stadium capacity = 40,000 W = Wolverton seats M = Manteca seats W + M = 40,000 PW = £20 – W/2000 PM = £ 10 W = 20,000 so PW = PM = £ 10 Is this the best you can do???

  6. Puzzle 3: Allocating Overhead Equal allocation of overhead

  7. Puzzle 4: Export Freedonia Steel? PFreedonia = $ 680 ACFreedonia = $ 400 PWorld = $ 375

  8. Poiuyts for Fun and Profit • P(x) = 6 – (3/5000) x • TR(x) = x [6 – (3/5000) x] MR(x) = Output effect + Price effect = [6 – (3/5000) x] - (3/5000) x MR(x) = 6–2(3/5000) x = 6–(6/5000) x • For linear demand relation, marginal revenue declines twice as fast as price (average revenue) as quantity increases.

  9. Poiuyts for Fun and Profit The cost side: TC (x) = 1000 + x + x2 /5000 = 1000 + x(1 + x/5000) = Fixed Cost + Variable Cost Variable Cost = Output x Avg Variable Cost Average Variable Cost = AVC = 1 + x/5000 • AVC increases as output increases MC(x) = (1+x/5000) + x(1/5000) = “Output effect” + “AVC Effect” MC(x) = 1 + 2x/5000

  10. Calcu_lating Poiuyt Profit TC (x) = 1000 + x + x2 /5000 What’s MC(x) ??? From dxn/dx = n xn-1 d(1000x0)/dx = 0x-1 = 0 No surprise:1000 doesn’t change when x changes d(1x1)/dx = 1x0 = 1 d(x2/5000)/dx = 2x1/5000 = 2x/5000 So MC(x) = 1 + 2x/5000 Using calculus, we get the same result as before

  11. Calcu_lating Poiuyt Profit Produce to point where MC = MR MC(x) = 1 + 2 x / 5000 MR(x) = 6 – (6/5000) x 1 + 2 x / 5000 = 6 – (6/5000) x 8 x / 5000 = 5 x = 25,000 / 8 = 3,125 When x = 3,125 P = 6 – (3/5000) x = 4.125 TR = (4.125 )(3,125) = 12,890.625 TC = 1000 + 3,125 + 3,1252 / 5000 = 6,078.125 Profit = 12,890.625 - 6,078.125 = 6,812.50

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