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Sedaia [141]
3 years ago
5

You are given the market demand function Q=2800-1000p, and that each duopoly firm's marginal cost is $0.07 per unit, which impli

es the cost function: C(qi)=.07qi, assuming no fixed costs for i= 1,2. The Cournot equilibrium quantities are: q1= _____; and q2 _____.
Business
1 answer:
Fed [463]3 years ago
3 0

Answer:

q1 = 910

q2 = 910

Explanation:

Given:

Q = 2800 - 1000p

Marginal cost = $0.07 per unit

Q = 2800 - 1000p

p = \frac{2800 - Q}{1000}

p = \frac{2800- q_1 - q_2}{1000}

Let's calculate profit of firm 1:

TR = p1 q1

= \frac{2800 q_1 - q_1^2 - q_1 q_2}{1000}

MR = \frac{2800 - 2q_1 - q_2}{1000}

MR = MC = 0.07

\frac{2800 - 2q_1 - q_2}{1000} = 0.07

Cross multiplying:

2800 - 2q₁ - q₂ = 70

2800 - 2q₁ = 70 + q₂

2800 - 70 - 2q₁ = q₂

2730 - 2q₁ = q₂...............(1)

Let's calculate profit of firm 2:

TR = p₁ q₂

= \frac{2800 q_2 - q_1 - q_2^2}{1000}

\frac{2800 - q_1 - 2q_2}{1000} = MR

MR = MC = 0.07

\frac{2800 - q_1 - 2q_2}{1000} = 0.07

Cross multiplying:

2800 - q₁ - 2q₂ = 70

2800 - 2q₂ = 70 + q₁

2800 - 70 - 2q₂ = q₁

2730 - 2q₂ = q₁................... (2)

Substitute 2730 - 2q₂ for q₁ in (1)...

Thus:

2730 - 2q₁ = q₂

2730 - 2(2730 - 2q₂) = q₂

2730 - 5460 + 4q₂ = q₂

-2730 + 4q₂ = q₂

-2730 = q₂ - 4q₂

-2730 = - 3q₂

q₂ = -2730/-3

q₂ = 910

Substituting 910 for q₂ in (2):

2730 - 2q₂ = q₁

2730 - 2(910)= q₁

2730 - 1820 = q₁

910 = q₁

q₁ = 910

The Cournot equilibrium quantities are: q₁= 910; and q₂ = 910

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Answer:

Explanation:

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B. Some other colleges and universities have a policy of paying equal salaries to professors in all fields. At some of these schools, economics professors have lighter teaching loads than professors in some other fields. What role do the differences in teaching loads play

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Kenneth entered into a contract to sell his home to Valerie, who put down a $5,000 earnest money deposit. At the last minute, Va
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8 0
2 years ago
An individual has utility function U(x)=x1/4U(x)=x1/4 for salary, and is considering new job offer which pays $80,000 with a bon
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Answer:

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Certainty equivalent is solved by taking the inverse utility function from the expected utility of a random wealth variable

U(x) = x^1/4

U^-1(x) = x^4

U^-1(x) === x^4

CE(x) = x^4

Salary   Bonus   Total income   U(x)= x^(1/4)       P(x)        U(x)*P(x)

80000       0          80000               16.82                1/7             2.4

80000    10000     90000               17.32                1/7            2.47

80000    20000    100000              17.78                1/7            2.54

80000    30000    110000               18.21                 1/7            2.6

80000    40000    120000              18.61                 1/7            2.66

80000    50000    130000              18.99                1/7            2.71

80000    60000    140000              19.34                1/7             <u>2.76</u>

Sum                                                                                             <u>18.14</u>

CE(x) =  18.14^4

CE(x) = 108280.22

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5 0
3 years ago
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Tcecarenko [31]

Answer:

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21,000/280,000 = 0.075 = 7.5%

There will be an increase for: 14.29 - 7.5 =  6.79%

3 0
3 years ago
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