La Tierra Roja is a resort village in the Arbuckle Mountains

La Tierra Roja is a resort village in the Arbuckle Mountains. Given its enormous popularity among well-heeled recreational skiers, Olympic teams, and extreme sports enthusiasts, all of its beds are booked in the winter season and there are, on average, 1200 skiers in the village. Skiers stay at La Tierra Roja for an average of 10 days. A study done by the largest hotel in the village has shown that skiers spend an average of $50 per person on the first night and $30 per person on each additional night in local restaurants. The study also forecasts that – due to increased hotel prices – the average length of stay for the 2008 season will be reduced to 6 days. What will be the percentage change in revenues of local restaurants compared to last year (when skiers stayed for the full ten days)? Assume that the hotels continue to be fully booked.

Solution

revenue last year:

number of nights = 10. amount spent on 1st night = $50. additional nights = 10-1 = 9 nights. total amount spent on these 9 nights = 9*$30 = $270. total amount per person for 10 nights = $50+$270 = $320

total amount for 1200 skiers = 1200*320 = $384,000

this year:

number of nights = 6. amount spent on 1st night = $50. additional nights = 6-1 = 5 nights. total amount spent on these 5 nights = 5*30 = $150. total amount per person for 6 nights = 50+150 = $200.

total amount for 1200 skiers = 1200*200 = $240,000

change in revenue = $384,000 - $240,000 = $144,000

% change = change in revenue/revenue last year = 144000/384000 = 37.5%