Question

League Merger. Suppose there are three soccer leagues in Europe: English Premier League (E), Bundesliga (B) and La Liga (L). Let qE ,q B, and qL

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represent the number of teams produced each league, respectively. Demand for soccer teams is given by P(Q)=160−3Q where Q=q E +qB +qL is the total number of soccer teams in Europe. Each league faces the same constant marginal cost of production, MC=40. 1. Suppose that the leagues engage in Cournot competition by simultaneously choosing the number of teams q E ,q B , andq L
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a) Find the English Premier League's profit function, π E (q E ,q B ,q L )

Answer 1

To find the English Premier League's profit function in Cournot competition, calculate the total revenue and cost functions and subtract the cost from the revenue.

Step-by-step explanation:

To find the English Premier League's profit function, we need to understand the concept of Cournot competition. In Cournot competition, each league chooses the quantity of teams it wants to produce simultaneously. The profit function for the English Premier League can be calculated as follows:

1. First, we need to find the total quantity of teams in Europe (Q) by summing up the quantities produced by each league: Q = qE + qB + qL.
2. Next, we can find the total revenue (TR) for the English Premier League by multiplying the price (P) by the quantity (qE): TR = P(qE).
3. The cost function for the English Premier League is given by: TC = MCqE, where MC is the marginal cost of production.
4. Finally, we can calculate the profit function (πE) by subtracting the total cost from the total revenue: πE = TR - TC.

By substituting the given price function (P) and cost function (MC), you can evaluate the profit function for the English Premier League.