Reference no: EM133133651

There are 10 potential entrants into the market for tomatoes. All tomato growers are identical. They face a fixed cost of 500 if they choose to enter the market and then have a marginal cost of 10 per bushel of tomatoes produced. Those who enter the market produce a homogeneous tomato with demand P = 150 -2Q, where Q is the number of bushels. The entering firms compete according to Cournot competition. Before choosing quantities firms sequentially announce whether they are entering and pay their fixed cost if entering.

1. Suppose N firms enter the market. Since this is a symmetric Cournot model, we've shown earlier in the class that in Nash Equilibrium each firm will produce,

qN = (1/(N + 1))*((A -c)/B) .

So for this model,

qN = 1/(N + 1) *(150 -10)/2 = 70/(N + 1) .

Given this, what is the price of tomatoes and the total quantity of tomatoes produced as a function of N?

2. What is the profit of the entering firms as a function of N?

3. What is consumer surplus as a function of N?

4. In a free entry equilibrium, how many firms will enter the market?

5. What is the profit of the first firm to announce it will enter the market?

6. Suppose a social planner were to choose the number of firms to enter the market to maximize total welfare, how many firms would enter?