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

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.

Price Elasticity and MRTR = Px

TR = P x + x PMR = 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

Puzzle 1: Luxury Boxes

MC = $ 300,000

P = $1,000,000 when x = 25

Sell More Boxes ???

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???

Puzzle 3: Allocating Overhead Equal allocation of overhead

Widgets Gidgets Gadgets

Sales

Variable cost

120

70

160

90

70

55

Contribution

Overhead

50

40

70

40

15

40

Net profit 10 30 -25

Shut down gadgets ???Does Gadgets’ overhead go away???

Puzzle 4: Export Freedonia Steel?

PFreedonia = $ 680

ACFreedonia = $ 400

PWorld = $ 375

Poiuyts for Fun and ProfitP(x) = 6 – (3/5000) xTR(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.

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

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

Calcu_lating Poiuyt ProfitProduce 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 = 3,125When 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