Question

На рынке дуополии рыночный спрос отображается функцией Q= 195 - 2,5 P. Товары продают две фирмы A и B . уравнения их реакции на выпуск конкурента : qA = 60 - 0,4qB , qB=80 - 0,5Qa . Определите по какой цене будет продаваться товар

Answer 1

уравнениями:

Спрос Qd = 20 – P

Предложение Qs = 2P – 10

Где Q – объем спроса(d) или предложения (s), в штуках Р – цена в рублях.

1Найдите равновесную цену и количество товара

2Чему равна выручка продавцов в равновесии

3Что будет наблюдаться на рынке, если государство

зафиксирует цену на уровне 5 рублей?

Answer 2

I will try to answer your question in detail. On the market of duopoly, the market demand is represented by the function Q = 195 - 2.5 P. The goods are sold by two firms A and B. The equations of their reaction to the output of the competitor are: qA = 60 - 0.4qB, qB = 80 - 0.5qA. Determine at what price the product will be sold.

To find the equilibrium price and quantity, we need to solve the system of equations:

qA + qB = Q qA = 60 - 0.4qB qB = 80 - 0.5qA

Substituting the second and third equations into the first one, we get:

(60 - 0.4qB) + (80 - 0.5qA) = 195 - 2.5 P

Expanding and rearranging, we get:

0.9qA + 0.4qB = 55 - 2.5 P

Using the second equation, we can express qB in terms of qA:

qB = 150 - qA

Substituting this into the previous equation, we get:

0.9qA + 0.4(150 - qA) = 55 - 2.5 P

Simplifying and solving for qA, we get:

qA = 50 - 2.5 P

Using the third equation, we can express qB in terms of qA:

qB = 80 - 0.5qA

Substituting the value of qA, we get:

qB = 105 - 5 P

Now, we can use the demand function to find the equilibrium price:

Q = qA + qB = 195 - 2.5 P 50 - 2.5 P + 105 - 5 P = 195 - 2.5 P -5 P = 40 P = -8

The equilibrium price is -8. This means that the market is not viable, as the price is negative. This is because the demand function is downward sloping and the reaction functions are upward sloping, which implies that the firms have negative marginal costs. This is an unrealistic assumption, as the firms would incur losses by producing any positive quantity.

Therefore, the product will not be sold at any price, as the market is not feasible. This is a case of market failure.

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