Question

In order to counter Iran, the Trump Administration has been significantly increasing the number of troops and military hardware stationed in the Middle East. There is debate among foreign policy makers as to whether large increases to the military presence in the Middle East will work successfully in terms of encouraging Iran to back down.

Let’s assume that the president’s utility if the continued military increase is successful is 24,000. However, if the continued increase 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 increases troops will be successful is 0.30. Assume the costs of continuing to increase the military presence is 1500. 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

Let us first take note of the goen information in the question. We can note the following -

The president’s utility if the continued military increase is successful = 24,000

The president’s utility if the continued military increase is unsuccessful = -9,000

Probability that increases troops will be successful = 0.30

Costs of continuing to increase the military presence = 1500

Given the above infromation, if the President is rational and risk neutral, he will only choose to go ahead with the increased military action if the expected benefit of the same far exceeds the expected costs of the same.

The cost is given to us as 1500

Expected benefits can be calculated as -

(0.3 x 24000) + (0.7 x -9000) = 7200 - 6300 = 900

Since the expected benefits do not exceed the costs, the President would not go ahead with increased military action and would just stick to the status quo without any change.