Efficient allocation without the backstop: R1=120, R2=180, R3=270; P1=170, P2=230, P3=320; Q1=990, Q2=810, Q3=540.
The expected number of units per well is 0.6*0 + 0.2*1 + 0.2*9 = 2. The minimum price is the one for which the EV of drilling is zero. EV=0.6*(0) + 0.2*1*(P-50) + 0.2*9*(P-50) - 450 = 2*(P-50) - 450, so P = 275. Alternatively, the EV can be written as the expected number of units found times the price, less the cost of a well: 2*(P-50) - 450.
P3 drops to 275, leading to new royalties: R3=225, R2=150, R1=100. New prices and quantities: P1=150, P2=200, P3=275; Q1=1050, Q2=900, Q3=675.
The price in period 1 falls by $20. Total units found via exploration = 285. Total wells drilled = 285/2 = 142.5.
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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 05/14/2008
