Question

Problem 4: A newspaper is considering adjusting its advertising rates for the coming year. The possible payoffs for these strategies will vary according to demand as follows: Low demand (50%) Moderate demand (30%)High demand (20%) Raise rates by 50% -9 4 12 Raise rates by 20% -4 4 8 Hold rates constant -1 3 5 Reduce rates by 20% 1 2 4 a) What is the expected monetary value (EMV) of the best strategy? b) What is the expected value of perfect information (EVPI)?

Answer 1

Q4) Now, the Expected Monetary Value (EMV) is the amount of money/payoff you can expect to generate from a certain strategy/decision. To calculate it, we multiply the payoff by their respective chances of occuring i.e. probabilities and total the results. The best strategy is considered to be the one with the highest/maximum EMV.

i) Raises rates by 50% : EMV = (-9) * 0.5 + 4 * 0.3 + 12 * 0.2 = -4.5 + 1.2 + 2.4 = -0.9

ii) Raises rates by 20%: EMV = (-4) * 0.5 + 4 * 0.3 + 8 * 0.2 = 0.8

iii) Holds rates constant: EMV = (-1) * 0.5 + 3 * 0.3 + 5 * 0.2 = 1.4

iv) Reduces rate by 20%: EMV = (1) * 0.5 + 2 * 0.3 + 4 * 0.2 = 1.9

So, the highest EMV is in case of strategy iv. So, the best strategy is reducing the rate by 20% and the EMV = 1.9

b) The Expected Value of Perfect Information is the maximum amount one is willing to pay for extra information regarding a decision problem. It implies that if one has perfect information regarding the states of nature prior to making the decision, then what is the worth of this information. The formula is : EVPI = EV with PI - EV without PI,

where, EV without PI = maximum EVP which we determined earlier,

So, EV with PI = we choose the best/max payoff for each state of nature and multiply it by the respective probabilities for each state.

EV with PI = 1 * 0.5 + 2 * 0.3 + 4 * 0.2 = 0.5 + 0.6 + 0.8 = 1.9

So, EVPI = 1.9 - 1.9 = 0.

So, if one has perfect information regarding the states of nature, the expected value of that perfect information (EVPI) is equal to zero.