The case on the theory of industrial markets (version 6)

Situation 2
The company operates in the market duopoly, demand function for the market is:
Q = 34 - P
P = 34 - Q = 34 - (q1 + q2)
The cost of producing a unit of output in the industry market are the same for each company and is 6 den. u
The first company to maximize its profits must meet a condition MR1 = MC1, which allows to determine its production capacity of 6 thousand. Units. And she makes a profit of $ 10 cash. u, as shown in the table.
Questions and tasks:
1. Determine the total costs of each company:
TC1 = 6 * 6000 = 36,000
TC2 = 6 * 20333 = 121998

Total costs are determined by multiplying the volume of production and the value of unit costs.
Revenue from product sales for the first firm will be equal to the sum of income and expenses:
N = 36,000 + 10,000 = 46,000 den. u
In the context of a duopoly with the size of the profit maximization of revenue will be calculated using the following formula:
TR1 = Pq1 = (34-Q) q1 = 34q1-Qq1 = 34q1- (q1 + q2) q1 = 34q1-q12- q1q2 = 46
On this basis, we determine the output of the second firm:
q2 = (6 * 34 - 6 * 6 - 46) / 6 = 122/6 = 20.33
2. Determine the marginal cost for each firm:
MC1 = mc2 = 7.67

Determining the marginal cost in a duopoly will be based on the following formula:
MR = (34q1-q12 - q1q2) / q1 = 34 - q1-q2 = 34 - 6 - 7.67 = 20.33
3. Upon entering the industry market 2nd company, in order to optimize their profits, it has to fulfill the equality MR2 = MC2. The volume of production will be 3 thousand. Units., Which will be implemented in the market for the price of 6 rubles. We define the function of demand for products the 2nd company:
q2 = Q - q1
In this case, the first and second company will sell its products in the industry market at a price of 7 rubles.
The leader in the industry market will first firm that determine its function is implemented on the following items:
q1 = Q - q2
Total production in these conditions will be:
Q = 34 - 7 = 27 thousand. Units.
4. Create a table forecasting changes in output for each firm.
Table
Forecast changes in production volumes on the market
1 2 3 4 5 6 7 8 9 10
q1 6 6 6 6 7 7 8 8 9 10
q2 0 1 2 3 3 4 4 5 5 5
P 10 9 8 7 6 5 4 3 2 1