Question

Upon coming to office, President Obama has called for a review of U.S. policy in Afghanistan. Among the things that he needs to decide is whether or not to call for a “surge”: sending 30,000 extra troops to Afghanistan, which would double the U.S. contingent fighting against the Taliban-led insurgency. There is debate among military experts as to whether such a surge would work successfully in Afghanistan (as it appears to have in Iraq).

The president’s utility if the surge is successful is 24,000. However, if the surge is unsuccessful, the president’s utility would be -9,000. The president’s utility from the status quo is 0. Assume that the president believes that the probability that a surge would be successful is 0.30. If the president is rational (and risk neutral), what will he do? Explain why. (You must show any calculations in detail; make sure to properly label what it is you are calculating).

Answer 1

Solution:

The president, if doesn't call for surge, that is status quo = 0

We need to compare this utility with the expected utility derived from the surge by risk neutral president. If the expected payoff from the surge is higher than the status quo utility, surge shall be called for.

Expected utility from surge = Probability of successful surge*utility from successful surge + Probability of unsuccessful surge*utility from unsuccessful surge

Expected utility from surge = 0.3*24000 + (1 - 0.3)*(-9000)

Expected utility from surge = 7200 - 6300 = 900

Clearly, 900 > 0, that is, expected utility from surge call is greater than no surge, thus, the president will call for a 'surge'.