Question

The city of​ Belgrade, Serbia, is contemplating building a second airport to relieve congestion at the main airport and is considering two potential​ sites, X and Y. Hard Rock Hotels would like to purchase land to build a hotel at the new airport. The value of land has been rising in anticipation and is expected to skyrocket once the city decides between sites X and Y.​ Consequently, Hard Rock would like to purchase land now. Hard Rock will sell the land if the city chooses not to locate the airport nearby. Hard Rock has four​ choices: (1) buy land at​ X, (2) buy land at​ Y, (3) buy land at both X and​ Y, or​ (4) do nothing. Hard Rock has collected the following data​ (which are in millions of​ euros):                                                                                       Site X Site Y Current purchase price 26 22 Profits if airport and hotel built at this site 50 40 Sale price if airport not built at this site 12 7 Hard Rock determines there is a 50​% chance the airport will be built at X​ (hence, a 50​% chance it will be built at​ Y).

Answer 1

Solution

We will solve this problem using EMV.

Back-up Theory

EMV (Expected Monetary Value) Criterion

Under this criterion, for each decision option, the pay-offs under various States of Nature (SON’s) are multiplied by the respective probability to obtain the EMV for that decision option. i.e.,

If there are k decision options (strategies), D1, D2, ….., Dk, r States of Nature, S1, S2, ….., Sr, then, the EMV for Di = ∑[j = 1, r]{Pij x pj}, where Pij = pay-off for Di under Sj and pj = probability of Sj.

Then, the decision option which yields the maximum EMV is selected.

Now, to work out the answer,

In the given problem,

D1: Buy land at​ X, D2:Buy land at​ Y, D2: Buy land at both X and​ Y, D4: Do nothing.

S1: Airport is built at site X, S2: Airport is built at site Y

Pay-off Calculations [all figures in million euros]

Airport is built at site X and land is bought at site X: i.e., D1S1 combination:

a profit of 50.

Airport is built at site X but land is bought at site Y: D1S2 combination:

land at site Y has to be sold out incurring a loss of (22 - 7) = - 15 being the difference between the purchase price and the resale price.

Airport is built at site Y and land is bought at site Y: i.e., D2S2: combination:

a profit of 40.

Airport is built at site Y but land is bought at site X: D1S2 combination:

land at site X has to be sold out incurring a loss of (26 - 12) = - 14 being the difference between the purchase price and the resale price.

Airport is built at site X and land is bought at site X and site Y:

i.e., D3S1 combination: a profit of 50 from site X less loss due to resale of land at site Y = 50 – (15) = 35.

Airport is built at site Y and land is bought at site X and site Y: D3S2 combination:

a profit of 40 from site Y less loss due to resale of land at site X = 40 – (14) = 26.

For D4, the pay-off is zero under both S1 and S2.

EMV Calculations

Di	Pay-off		EMV
	S1	S2
D1	50	- 14	18
D2	- 15	40	12.5
D3	35	26	30.5
D4	0	0	0
Pj	0.5	0.5

Conclusion

Since EMV of 30.5 is maximum, the optimum decision is D3,

i.e., to buy land at both sites. ANSWER