1. Stadium Algebra P W = 20 – W / 2000 { Gotta lower price to Wolverton fans Δ P W = – ΔW / 2000 a bit to sell them another seat.} TR W = P W W Δ TR W = Output Effect + Price Effect + {Revenue when you - {Reduced price on all the sell another seat} seats you’ve already sold} = (20 – W / 2000) ΔW – W (ΔW / 2000) MR W = ΔTR W / ΔW = 20 – W / 2000 – W / 2000 MR W = 20 – 2 W / 2000 Want MR W = MC = 10 so 20 – W/1000 = 10 = P M Solution: W = 10,000 ; P W = 15 ; TR W = 150,000 M = 30,000; P M = 10 ; TR M = 300,000

2. 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

3. Poiuyt Algebra P(x) = 6 – 3 x / 5000 ΔP = - 3 Δx / 5000 TR = Px = (6 – 3 x / 5000)x ΔTR = P Δx + x ΔP =(6–3x/5000) Δx – 3x Δx/5000 MR = ΔTR / Δx MR=6 – 3x/5000 – 3x/5000 MR = 6 – 6 x / 5000 TC(x) = 1000 + x + x 2 /5000 = 1000 + (1 + x/5000)x = Fixed + {Avg Variable}x = FC + {AVC } x ΔTC ={AVC}Δx + x Δ{AVC} =output effect + cost effect Δ{AVC} = + Δx / 5000 ΔTC=(1+x/5000)Δx + x Δx/5000 ΔTC = (1 + 2x/5000)Δx MC=ΔTC/Δx MC = (1 + 2x / 5000)

4. Poiuyt Solution Equate marginal revenue to marginal cost: MR = 6 – 6x / 5000 = 1 + 2x / 5000 = MC 8 x / 5000 = 5 x = 25000 / 8 = 3125 P(3125) = 6 – (3/5000)3125 = 6 – 1.875 P = 4.125 TR = Px = (4.125)(3125) = 12,891 TC(3125) = 1000 + (1 + 3125/5000)(3125) = 1000 + (1.625)(3125) = 1000 + 5078 = 6,078 Profit = TR – TC = 12891 – 6,078 = 6,813

5. Poiuyts and Qwerts: Substitute Goods A firm produces and sells poiuyts and querts (which are left-handed poiuyts) TC = 10x p + 20x q + 1000 Sales of querts drive down the price of poiuyts Sales of poiuyts drive down the price of qwerts P p = 90 – x p /100 – x q /300 P q = 120 – x q /100 – x p /150 When there is no capacity constraint, produce each good to the point where its marginal profit = 0. Note: MR p = P p + x p {ΔP p / Δ x p } + x q {ΔP q / Δ x p } MR q = P q + x q {ΔP q / Δ x q } + x p {ΔP p / Δ x q } where ΔP p / Δx p, ΔP q /Δx p, ΔP q /Δx q, ΔP p /Δ x q are all negative.

6. 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

7. Puzzle 3: Allocating Overhead Equal allocation of overhead WidgetsGidgetsGadgets Sales Variable cost 120 70 160 90 70 55 Contribution Overhead 50 40 70 40 15 40 Net profit1030-25 Shut down gadgets ??? Does Gadgets’ overhead go away???

8. Puzzle 4: Export Freedonia Steel? P Freedonia = $ 680 AC Freedonia = $ 400 P World = $ 375