Question

In: Economics

Two profit maximizing oligopolists produce electricity. They set their productions levels,y1 and y2, simultaneously.p(y) = 10−y,...

Two profit maximizing oligopolists produce electricity. They set their productions levels,y1 and y2, simultaneously.p(y) = 10−y, where y=y1+y2. Assume the cost curve for firm 1 and firm 2 are C(y1) = 2y1 and C(y2) = 2y2 respectively. Marginal cost for each firm is constant at 2.

Suppose firm 1 and firm 2 decide their output simultaneously.

1. Write down each firm’s profit maximization problem.

2. Determine each firm’s best response function (i.e BR1(y2) and BR2(y1)) and plot it on a graph.

3. Determine the optimal (equilibrium ) levels of production y^Co_1 and y^Co_2.

4. Determine the Consumer Surplus, Producer Surplus and Dead weight loss.

Expert Solution

Answer summary:

(1) π₁ = 8y₁ - y₁² - y₁y₂ and

π₂ = 8y₂ - y₂² - y₁y₂

(2) BR₁(y₂) : y₁ = 4 - (y₂/2) and

BR₂(y₁) : y₂ = 4 - (y₁/2)

(3) y^Co_1 = 2.67 and y^Co_2 = 2.67

(4) C.S. = 14.2578

P.S. = 24.8844

D.W.L. = 10.8578

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Rahul Sunny answered 3 years ago

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