Question

JR Ewing, a Texas oil driller, estimates his present wealth to be $20 million. He obtains a lease to drill in Dallastown where he estimates that the cost of drilling will be $10 million, and there is a 20 per cent chance that oil valued at $100 million will be discovered.

(i) What is the expected net gain of drilling in Dallastown?

(ii) If JR’s utility function is U(W)=ln W, where W is his wealth in millions of dollars, will he undertake the drill?

(iii) JR’s brother, Bobby learns about the lease that JR has obtained and tries to persuade him to let him have a 50% share in the venture. In other words, Bobby asks that he be allowed to get half the revenues in exchange for putting up half the monies needed for drilling. Will JR let Bobby into the deal? What principal of the economics of uncertainty does your answer illustrate?

Answer 1

i ) Net gain from drilling =0.2*100 + 0.8* (-10) = 12

ii ) Net utility from current wealth = 2.995732274 Expected utility = 0.2* ln (110) + 0.8* ln (90) = 4.5399 Since Expected utility from drilling is higher than the current utility. He will undertake the drill

iii ) Expected utility after Bobby's offer =0.2*LN(65)+0.8*LN(15) JR won't let bobby into the deal as it is reducing his utility. The answer illustrates the Completeness principle as JR can measure utility under various scenarios