Tourist Trap Model with Downward-Sloping Demand Curve
ECON0402 - Term paper
Tourist Trap Model with Downward-Sloping Demand Curve
2010 97 0203
Introduction
This paper will attempt to relax the unitary demand assumption of the tourist trap model that we saw in class. The others assumptions are conserved.
We will now have a linear downward-sloping demand-curve: p=G-gq I will first discuss what could be the equilibrium price and how we can deduce it.
Then, I will explain the conditions that must be fulfill to sustain this equilibrium.
Finally, I’ll discuss the economic interpretation of these conditions.
Equilibrium price
Since we now consider a downward sloping demand curve, the quantity the consumer will buy could be more than 1 and will depends on the price. Therefore, a relevant measure to compare consumer choices would be the consumer surplus.
To simplify the following demonstrations, I will use the following convention:
Consumer surplus=fp=12(G-p)q(p) `
I assume in the following analysis that the consumer will buy in the shop, whatever the price is, a quantity depending on his demand function and that as long as his surplus is maximized.
Equilibrium at p = MC?
Let’s suppose first that the firms all charge p=MC. If one firm charges p’ such as: f(p ')<fp-c
Then the unfortunate consumer will still buy in this shop since it would results in a lower surplus if he tries to search for another shop. Therefore, as in the more simplified model, p = MC is not a feasible equilibrium.
Monopoly price as an equilibrium price
We will now consider the single price equilibrium at the monopoly price and try to find if it would be profitable for a single firm to deviate from the equilibrium.
Consider n-1 shops practicing the monopolist price pm and a single shop practicing a lower price p '.
If the consumer is lucky enough to find the cheaper shop right away, he will buy according to his demand curve and his surplus will be fp '
On the other hand, the unlucky consumer will still buy in the
Tourist Trap Model with Downward-Sloping Demand Curve
2010 97 0203
Introduction
This paper will attempt to relax the unitary demand assumption of the tourist trap model that we saw in class. The others assumptions are conserved.
We will now have a linear downward-sloping demand-curve: p=G-gq I will first discuss what could be the equilibrium price and how we can deduce it.
Then, I will explain the conditions that must be fulfill to sustain this equilibrium.
Finally, I’ll discuss the economic interpretation of these conditions.
Equilibrium price
Since we now consider a downward sloping demand curve, the quantity the consumer will buy could be more than 1 and will depends on the price. Therefore, a relevant measure to compare consumer choices would be the consumer surplus.
To simplify the following demonstrations, I will use the following convention:
Consumer surplus=fp=12(G-p)q(p) `
I assume in the following analysis that the consumer will buy in the shop, whatever the price is, a quantity depending on his demand function and that as long as his surplus is maximized.
Equilibrium at p = MC?
Let’s suppose first that the firms all charge p=MC. If one firm charges p’ such as: f(p ')<fp-c
Then the unfortunate consumer will still buy in this shop since it would results in a lower surplus if he tries to search for another shop. Therefore, as in the more simplified model, p = MC is not a feasible equilibrium.
Monopoly price as an equilibrium price
We will now consider the single price equilibrium at the monopoly price and try to find if it would be profitable for a single firm to deviate from the equilibrium.
Consider n-1 shops practicing the monopolist price pm and a single shop practicing a lower price p '.
If the consumer is lucky enough to find the cheaper shop right away, he will buy according to his demand curve and his surplus will be fp '
On the other hand, the unlucky consumer will still buy in the