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Amusement parks and ski resorts typically charge a one-time entry fee to use as many rides or ski-lifts as people can in a day. They do not charge a fee for every individual ride that a person takes. Barro and Romer analyze why amusement parks and ski resorts use this type of entry fee pricing.
In this paper, Barro and Romer discuss how during peak seasons, amusement parks (ski-lift services, etc.) are very crowded and have long lines. If an amusement park is crowded, and has “chronic queuing,” economists would suggest that the park would be better off if they raised prices. Traditionally raising prices when demand is high will bring the park to an efficient equilibrium where supply is equal to demand. Economist would also suggest that if the price were too low, there would be other inefficiencies that would occur in the park. Parks that have long lines continue to thrive, even though economists say they should not be.
The authors argue that amusement parks and ski-lift services that set prices so that lines are longer during peak times are not being inefficient. They are maximizing profits in equilibrium by setting prices for all-day use subject to a downward-sloping demand curve. As demand increases, it may not even cause the park to increase prices, as prices are sticky. The authors analyze different conditions such as park congestion, transportation ability, park quality, and how those factors affect pricing.
There are two types of agents in this economy: Individuals and amusement park (ski-lift service, etc.) firms.
Each individual’s objective is to maximize their utility. They want to get the most out of their experience at the amusement park. If a park is charging for each individual ride, the individual tries to maximize utility:
where qi is the number of rides, and zi is goods other than rides. The individual chooses qi to maximize the utility subject to
Yi=Pqi+zi+ci, where Yi is the real income, ci is the entry fee, and P is the price per ride. The individual is maximizing their utility subject to a budget constraint. There is no entry fee, but there is a price per ride with ride tickets.
For an individual that is being charged an entry fee with no extra price per ride, they are also attempting to maximize utility subject to their budget constraint. Price per ride is equal to zero, but there is an entry fee.Individuals are also constrained by preferences, transportation costs, and congestion aversion. The individual can also choose other ski areas or amusement parks.
The firm’s objective is to maximize profits. They can choose what price to charge, and if they want to charge an entry fee or charge for individual rides. They are constrainedby a production function (capacity for the ski area or amusement park).
This model assumes that ski lifts and amusement parks are competitive. Under a competitive equilibrium each agent will maximize their objective. The park will maximize their profits and the individual will maximize their utility. All markets will need to clear.
For ride ticket pricing, “equilibrium requires that the total capacity of rides, Jx, equal the total number demanded, qN – that is,
Jx = D(P) × N(P,s).”
The price is determined by a given value of Jx. Total capacity increases, price will fall. If demand increases, prices will rise.
For entry fee equilibrium there are several equations that need to be satisfied. In this model, each individual’s preferences are the same. This model means that parks and ski resorts set their prices to maximize profits, given the demand of the individuals. Individuals are attempting to maximize their utility, given the prices the ski resorts and amusement parks set.
The equilibrium conditions for single-ride tickets and all day entry fees initially provide the same result. Each firm will be able to maximize their profit and each individual will be able to maximize their utility. Barro and Romer account for a few more factors that could impact the results. The factors that were not included initially were costs incurred to avoid theft of rides, the heterogeneity of rides (not every ride will be the same depending on time of day, breakdown of equipment, congestion, etc.), and time spent waiting in line, which will have a positive opportunity cost.
If parks charged for each ride, there would also be higher costs associated with collecting money. The park would have to have a cashier (or another way of collecting money/tickets) at every ride. This would increase the cost for the park. The model predicts that charging a one-time entry fee will be more efficient for both the individual and for the firm.
The authors suggest that that this model can be used for fishing. If there is a price per fish for the fisherman, it will be less effective than a fishing license where a fisherman can catch as many fish as he wants in a given period of time.
This model can also be used when thinking of a gym. When you go to they gym you pay for a specific amount of time you are able to use the gym. Most people pay per month, and they have unlimited access after the initial payment. The gym does not charge for every machine that you use or every weight that you lift. This would fit with the model because it is more efficient to charge a one-time fee for a certain amount of time.
When applying the gym to this model, each individual’s objective is still to maximize their utility subject to a budget constraint. The gym is trying to maximize their profits subject to a production constraint (gym capacity).
This paper helped me understand why certain types of industries charge a one-time fee instead of a per-use charge. The main reason for using this type of pricing seems to be because it costs less to both the firm (costs less money), and to the consumer (costs less time). This will increase the firm’s profits and the consumer’s utility. This model will be useful for many industries to determine the most efficient form of pricing.
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