ECO 313: Market Structure Analysis: Cournot Duopoly and N-Firm Model

This assignment analyzes the Cournot duopoly and N-firm models, exploring market structures and business regulations. It begins with a Cournot duopoly model involving two firms, calculating their best response functions, outputs, total revenues, costs, and profits under symmetric and asymmetric cost conditions. The analysis then extends to the N-firm Cournot model, examining how the number of firms impacts industry output, price, market power, and individual firm profits and market shares. The assignment further investigates the free market equilibrium, determining the number of firms and price level where profits are zero. The comparison is made between the two models in terms of output, price, and profit. The analysis uses derivatives to maximize profits and employs formulas to calculate market power and market share. The findings demonstrate how changes in cost parameters and the number of firms affect market outcomes, providing insights into competitive dynamics and market equilibrium.

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ECO 313 MARKET STRUCTURE AND BUSINESS
REGULATIONS

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1. The Cournot duopoly is a model where two players produce output. The general
formula that has been used for the calculation is below:
The industry demand curve is given by p= 300-Q
Now the cost functions of the firms are given as TC= 3Q1+3Q2+100
Now the profit of the first firm is Q1(300-Q1-Q2)-3Q1-3Q2-100
Taking the derivative with respect to Q1 taking Q2 constant and setting the derivative for
0 we have,
300-2Q1-Q2-3=0
 Q1= (297-Q2)/2
This is the best response function of the firm 1.
 Similarly the best response function of the firm 2 is Q2= (297-Q1)/2
Putting these value and equating them in the excel sheet the calculations are done. The
total revenue and costs of each of the firms are subsequently found out using the formula
of, profit = TR-TC. This was a case of symmetric cost function and hence the output of
one firm is similar to the other.
2. Now the cost parameters of the first firm are changed. D1 is increased to 5, E1 is
reduced to 2 and the f1 is increased to 250. That means the cost of production for the
firm 1 is increased while there is no change in the cost of the firm 2.
The new equilibrium production for firm 1 has reduced from 99 to 97.67 whereas the
production for the firm 2 has increased to 99.67. Therefore the overall production has
dropped to 197.33 from 198. The Total revenue of firm 1 has reduced while on the
other hand the total revenue of the firm 2 has increased since the last case. The new
total revenues are Total Revenue 1 = $10,027.11and Total Revenue 2 =$10,232.44
respectively. The total cost of the firm 1 is now $937.67 and the total profit is reduced
to $9,089.44. On the other hand the cost of the firm 2 is $692.00 and the total profit is
$9,540.44.
3. Now in that case if the cost parameters of the firm 2 changes the there will be many
changes in the model. Now in this case the d2 is increased to 6, the e2 is reduced to 1
and the f2 is increased to 300. This means there has been an overall rise in the cost for

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the firm 2. Now due to that the production of the firm 1 increase to 100 and the
production for the firm 2 reduce to 97. Therefore the overall production of the market
has fallen to 197 from 198 in the previous case. The new price has also increased
from $102 to $103. The total revenue of the firm 1 has increased to $10,300.00 and
the total revenue of the firm 2 has reduced to $9,991.00. The cost of the firm 1 has
reduced to $691 while on the other hand the cost of the firm 2 has increased from
$694 to $982.00. The profit of the firm 1 is now $9,609.00 whereas the profit of the
firm 2 has reduced to $9,009.00.
4. Now each firms output is calculated in the n-firm Cournot model by maximising the
profit of the firm. Now the profit is,
Q1(100-0.00005*Q1)-12-9*Q1
Taking the derivative with respect to Q1 and setting it to 0 we have,
100-0.0001Q1-9=0
Therefore Q1= (100-9)/0.0001
Industry output is calculated by multiplying the number of firms with each firms
output.
The Industry price is calculated by putting the industry price on the demand equation
which is P= 100-0.00005Q1. The market power is calculated by using the formula,
market power= (P-MC)/P where P is the price charged by the firm and MC= is the
marginal cost of the firm. Each firms profit is the product of the revenue and the
price. The market share is determined by dividing the each firms output by the
industry output. And lastly the free market equilibrium would be where the price is
equal to MC. Therefore, the putting MC in the equation of P= 100-0.00005Q1 we
have the equilibrium in case of the free market.
5. Now if the number of firm increases in the market from 1 to 7 the industry output
increases and price drops to $99.98. However the change in the market power is very
slight. There is also a reduction in the profit of each of the sellers as well. Lastly with
the increase in the number of firm, the market share of the firms also reduces. The
control over the prices of each firm reduces as the number of firm increases.
Therefore as the number of firm increases it tends to become a perfectly competitive
market.
6. Now in order to determine the free market equilibrium, the profit of the sellers needs
to be 0 that means where there is only a normal profit in the market. Now in order to
calculate that a solver has been used where the value of the price has been set to 0

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changing the number of firms in the market. The analysis finds out that, in a free
market there would be 36304 number of firms and the price level would be $9.24.
Equating with the industry level production, the free market equilibrium production
would be 1815200.
7. A) The formula used for the calculations of the Q1 and the Q2 is the derivative of the
profit which is,
Profit= Total revenue – total cost
After that the derivative has been set to the value 0 in order to get the value of Q.
The calculation of the profit is Total revenue- Total cost.
b) The output in case of the duopoly cournot model is lesser than that of the other
model. The price is also slightly different between the two models. The price in case
of the cournot duopoly model is $102 while the price for the n firm cournot model is
$100. In addition to that the profit is also a lot more in case of the n firm duopoly
model as has been found in the analysis. Due to the presence of 2 firms in the n firm
cournot model the market share is 50%.