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The Mantra: MR = MC

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.

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The Mantra: MR = MC

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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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