Ec370: A model of Innovation what is an idea? . An idea is a pair ( v , c ) V: Value given by consumer surplus in a competitive market with o marginal Cost. P * Area below D, P = marginal Cost but above eqprice C. 5. = V MC= 0 = S * Value per-period of D time . P+ C: cost ( fixed ) of developing the idea into an innovation e.g. RXD , Prototyping ,... C A ( Vs, 63 ) ( v . , CI ) Vz z V, ( Vzizz ) idea 3 idea 1 "Better " idea 2 V Idea 3 has a higher Cost than 1* 2 , but higher Value as well Define . M: Share of V captured by consumers/users. TL: Share of V captured by producers / innovators R : Share of V that is deadweight loss .L caused by distortions such as market power taxes , ... M + TC + & = 1 m XV : Total Per-period Value to consumers TC * V . Total Per-period Value to Producers l * v . Total Per- Period 'DWL . m . V + TC * V + ex V = ( m+ TC + 1 ) V = V Monopoly : Suppose marginal Cost = 0 P PA - b Q2 (S = MV Profit maximization Di PS = TCV choose Q such that TR = Q X P DWL = QV 1, marginal revenue = Q ( A - bQ ) MC = 0 1 1 = AQ - bQ2 D " marginal cost MR = TR' f A - 26Q Profits: Total Rev - Total cost M C : U MR - willing to buy ch. in profits : MR - MC at p' but y=mx +b not p+ (actual Ch. is slope price ) profite Y = P P'> Mc * = Q - profitable could happen but don't due to market Power . P P= MC Individual firm (S = M V = V in competitive mkt m= 1 2 : 0 TL : 0 MC P : 11 D = MR MC=S P+ D - QP+ ( vic) In a competitive mkt, P - MC. 0 profits innovation cast ( v , c ) Total profits = 0-c co - rather not innovate Time Horizon V is per period . R : Effective Value of the Length of lifespan L Intuitively : Lifespan in Value of time. RXV lifetime Value T: Smalles of two values : R ( lifespan ) and the length of time of any IP Protections utility patent : 20 years Design Patent : 15 years Copyright : Death + 70 years Trademark : Indefinite when enforced.Efficient Investment in ideas . Idea : A pair ( v , ( ) C V: value (per-period ) C : Fixed cost of development Divided V into shares m: shore of value captured by consumers It: share of Value captured by producers e: uncaptured share m+ Tite = 1 No capital constraints: unlimited $ $ Efficient to invest : R (It m ) V- c 20 - CC/R ( FC +m ) y Inefficient R ( TC + m )V " R ( TL + M ) V I per- period Ideas valve 1 1 NC Invest Invest value captured Efficient per period Ideas 1 1 = in the ideal world V & = 0 Measure of lifespan Important Question: Which ideas will in ? be invested . The above is which should be invested inNOT R ( Term ) V- c 20 what T is ? Profitable Lifspan ming R , IP / mkt power protections's - The profitable lifespan what terms should be included : TC , T, VIC. Profitable to invest ( will invest ) if +TV - L 20 CC TTCV unprofitable NOT Invest Invest Profitable T CR 2 2 3 4 ( 5 TC L TC TM Intuition TIV CR ( TIM )V 2x 4 R ( TC + M ) V T , TCV under TI T, fells to Tz Leg Congress shortens patent life)- Investments under TI shortens patent life ) - Investments T2 TCV The share of profitable under Tz ideas falls Fewer efficient innovations will occur T2 TV C profitable but inefficient 12 ( TC + m ) V TI rises to In Leg Congress increases TITCV potent life significantly T, > R Prevents future investment Policy Goal : Optimal choice of TI