In the next few weeks, Congress is going to decide whether or not to develop an expensive new weapons system. If the system is approved, it will be very profitable for the defense contractor, General Statics. Indeed, if the new system is approved, the value of stock in General Statics will rise from $10 per share to $15 a share, and if the project is not approved, the value of the stock will fall to $5 a share. In his capacity as a messenger for Congressman Kickback, Buzz Condor has discovered that the weapons system is much more likely to be approved than is generally thought. On the basis of what he knows, Condor has decided that the probability that the system will be approved is 3/4 and the probability that it will not be approved is 1/4. Let cA be Condor’s consumption if the system is approved and cNA be his consumption if the system is not approved. Condor’s von Neumann-Morgenstern utility function is U(cA, cNA) = .75 ln cA + .25 ln cNA. Condor’s total wealth is $50,000, all of which is invested in perfectly safe assets. Condor is about to buy stock in General Statics.
(a) If Condor buys x shares of stock, and if the weapons system is approved, he will make a profit of $5 per share. Thus the amount he can consume, contingent on the system being approved, is cA = $50, 000+5x. If Condor buys x shares of stock, and if the weapons system is not approved, then he will make a loss of _______ per share. Thus the amount he can consume, contingent on the system not being approved, is cNA = ________.
(b) You can solve for Condor’s budget constraint on contingent commodity bundles (cA, cNA) by eliminating x from these two equations. His budget constraint can be written as _____ cA+ ______ cNA = 50, 000.
(c) Buzz Condor has no moral qualms about trading on inside information, nor does he have any concern that he will be caught and punished. To decide how much stock to buy, he simply maximizes his von Neumann- Morgenstern utility function subject to his budget. If he sets his marginal rate of substitution between the two contingent commodities equal to their relative prices and simplifies the equation, he finds that cA/cNA ________. (Reminder: Where a is any constant, the derivative of a ln x with respect to x is a/x.)
(d) Condor finds that his optimal contingent commodity bundle is (cA, cNA) = ______. To acquire this contingent commodity bundle, he must buy ______shares of stock in General Statics