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Lee,Wilde (1980) - Market Structure And Innovation A Reformulation (view source)
Revision as of 21:18, 17 November 2010
, 21:18, 17 November 2010no edit summary
The expected benefits are (supposed the same as in [[Loury (1979) - Market Structure And Innovation |Loury (1979)]]):
:<math>\mathhbbmathbb{E}B = \int_0^{\infty} pr(\hat{\tau_i} = t) \left ( \int_0^t pr(\tau=s) V e^{-sr} ds \right) dt\;</math>
:<math>\therefore \mathhbbmathbb{E}B = \int_0^{\infty} a e^{-at} \left ( \int_0^t h e^{-hs} V e^{-sr} ds \right) dt \;</math>
:<math>\therefore \mathhbbmathbb{E}B = \frac{Vh}{a+h+r}\;</math>
===Modelling Costs===
Expected costs are thus:
:<math>\mathhbbmathbb{E}C = \int_0^{\infty} \left \int_0^{t} x e^{-rs} ds \right \cdot pr(\hat{\tau_i} = t or \tau_i = t) dt + F\;</math>
:<math>\therefore \mathhbbmathbb{E}C = \int_0^{\infty} \left \int_0^{t} x e^{-rs} ds \right \cdot (a+h) e^{-(a+h)t} dt + F\;</math>
:<math>\therefore \mathhbbmathbb{E}C = \frac{x}{a+h+r} + F\;</math>
Expected profit is expected benefit minus expected cost:
:<math>\mathhbbmathbb{E}\pi = \frac{Vh - x}{a+h+r} - F\;</math>
