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

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.

Solutions

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

Please refer to following two images for full answer:

Rahul Sunny answered 2 years ago

Next > < Previous

Related Solutions

Two profit maximizing oligopolists produce electricity. They set their productions levels,y1 and y2, simultaneously. p(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 is the leader and sets the quantity first. Firm 2 is the follower. (Stackelberg) 1. Write down each firm’s profit maximization problem 2. Determine the optimal (equilibrium ) levels of...

The joint density of Y1, Y2 is given by f(y) = k, −1 ≤ y1 ≤...

The joint density of Y1, Y2 is given by f(y) = k, −1 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1, y1 + y2 ≤ 1, y1 − y2 ≥ −1, 0, otherwise a. Find the value of k that makes this a probability density function. b. Find the probabilities P(Y2 ≤ 1/2) and P(Y1 ≥ −1/2, Y2 ≤ 1/2 c. Find the marginal distributions of Y1 and of Y2. d. Determine if Y1 and Y2 are independent e....

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t...

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1 describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). Use a graphing device to draw the triangle with vertices A(1, 1), B(4, 3), C(1, 6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.)

Two waves y1(x,t) and y2(x,t) propagate in the air: y1 = A sin(6x - 12t) y2...

Two waves y1(x,t) and y2(x,t) propagate in the air: y1 = A sin(6x - 12t) y2 = A sin(5x - 10t) Find: a) The equation of the resulting pulse, y1 + y2. b) The distance between 2 consecutive zeros in the elongation. c) The distance between 2 consecutive absolute maxima of the elongation.

(1 point) In general for a non-homogeneous problem y′′+p(x)y′+q(x)y=f(x) assume that y1,y2 is a fundamental set...

(1 point) In general for a non-homogeneous problem y′′+p(x)y′+q(x)y=f(x) assume that y1,y2 is a fundamental set of solutions for the homogeneous problem y′′+p(x)y′+q(x)y=0. Then the formula for the particular solution using the method of variation of parameters is yp=y1u1+y2u2 where u′1=−y2(x)f(x)W(x) and u′2=y1(x)f(x)W(x) where W(x) is the Wronskian given by the determinant W(x)=∣∣∣y1(x)y′1(x)y2(x)y′2(x)∣∣∣ So we have u1=∫−y2(x)f(x)W(x)dx and u2=∫y1(x)f(x)W(x)dx. NOTE When evaluating these indefinite integrals we take the arbitrary constant of integration to be zero. In other words we have...

Determine which of the following pairs of functions y1 and y2 form a fundamental set of...

Determine which of the following pairs of functions y1 and y2 form a fundamental set of solutions to the differential equation: x^2*y'' - 4xy' + 6y = 0 on the interval (0, ∞). Mark all correct solutions: a) y1 = x and y2 = x^2 b) y1 = x^2 and y2 = 4x^2 c) y1 = x^2 and y2 = x^3 d) y1 = 4x^2 and y2 = x^3 e) y1 = [(x^2)+(x^3)] and y2= x^3

13-) In a Cournot duopoly, firms 1 and 2, produce Y1 and Y2, respectively. They have...

13-) In a Cournot duopoly, firms 1 and 2, produce Y1 and Y2, respectively. They have identical total cost function C(Yi) = 2 Yi, i = 1, 2. The market demand function is Y = 20 - p, where Y = Y1 + Y2. The market price p in a Cournot equilibrium is: Select one: a. 8 b. 20 c. 12 d. 4 14-) Which of the following is not a decision faced by a firm in a perfectly competitive...

Determine the profit maximizing quantity and profit levels; and then graph (in general form) the outcomes...

Determine the profit maximizing quantity and profit levels; and then graph (in general form) the outcomes for the production function ( standard form with q(K,L) curve ) , cost/revenue functions (with MC, AC, and P curve/line) and profit function ( profit (q) curve ) for the following all graphs have to display q*: 1. C(q)=1000+q^2, P=10000 2. C(q)=1000+4q^3, P=10000 3. C(q)=1000+q^1.5, P=10000 4. Explain the differences between your outcomes and give a plausible reason for the difference between 1 &...

The set R^2 with addition and scalar multiplication defined by (x1, y1) + (x2, y2) =...

The set R^2 with addition and scalar multiplication defined by (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) c(x1, y1) = (cx1, y1) is not a vector space. Determine which axiom fails and find a counterexample that shows that it fails.

Let x,y ∈ R3 such that x = (x1,x2,x3) and y = (y1,y2,y3) determine if <x,y>=...

Let x,y ∈ R3 such that x = (x1,x2,x3) and y = (y1,y2,y3) determine if <x,y>= x1y1+2x2y2+3x3y3 is an inner product

Subjects