Market Structure, Business Regulations, and Merger Strategies

This assignment solution analyzes market structures and business regulations using a Cournot duopoly model. It examines the profit-maximizing strategies of firms in different scenarios, including non-merged, merged, and partially merged structures. The solution calculates profits for upstream and downstream firms, considering factors like industry price, revenue, and costs. The analysis explores the implications of vertical mergers, highlighting how they can impact operational costs, profit margins, and market prices. The assignment concludes that vertical mergers can be a Pareto optimum solution in a Cournot duopoly model, leading to lower market prices and increased consumer surplus, but two vertical mergers could reduce production. The solution also provides insights into the rationality of different merger strategies, including the potential for downstream firms to exit the market in certain scenarios.

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MARKET STRUCTURE AND BUSINESS REGULATIONS

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Contents
Question 1..................................................................................................................................3
Question 2..................................................................................................................................4
Question 3..................................................................................................................................4
Question 4..................................................................................................................................5
Reference....................................................................................................................................7

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Question 1
a. The firm1d’s q1= (77-q2d-q1u-q2u-p1u)/2
The firm2d’s q2= (77-q1d-q1u-q2u-p1u)/2
After that industry price has been calculated from the inverse demand function and
subsequently, the revenue and the cost which is 23*q1d-p1u*q1d has been calculated in
the spreadsheet.
General equation of industry price= 100-q1d-q2d-q1u-q2u
General equation for profit of firm 1 is (100-q1d-q2d-q1u-q2u)*q1d-23*q1d-p1u*q1d
Where p1u is the upstream price charged by the upstream firms of the model.
General equation for profit of firm 2 is (100-q1d-q2d-q1u-q2u)*q2d-23*q2d-p1u*q2d
Where p1u is the upstream price charged by the upstream firms of the model.
b. The firm2u’s q1u= (77-q2d-q1u-q2u)/2
The firm2u’s q2u= (77-q1d-q1u-q2u)/2
After that upstream price has been calculated from the inverse demand function and
subsequently, the revenue and the cost which is 23*q1u has been calculated in the
spreadsheet.
General equation of upstream price= 100-q1u-q2u
General equation for profit of firm 1u is (100-q1d-q2d-q1u-q2u)*q1u-23*q1u
General equation for profit of firm 2u is (100-q1d-q2d-q1u-q2u)*q2u-23*q2u
In this case the cost price of the upstream firms is only the unit cost of which the
parameters have been given as 23.
c. The general equations of profit are the difference between the Total Revenue and the
Total cost which for firms are equal to the amount found in the part 1.
The formula used in the part 1 is the,

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Profit= (100-q1d-q2d-q1u-q2u)*q1d-23*q1d-p1u*q1d
This for the firm 1d matches and is 58.77 as can be seen from the excel spreadsheet.
Similarly the value is same for the other three firms as well.
The profit of firm 1d= 58.77
The profit of firm 2d= 58.77
The profit of firm 1u= 475.34
The profit of firm 2u = 475.34.
Question 2
a. The general formula for the q1d= (100-q2d)/2
The general formula for the q2d= (100-q1d)/2
After that the industry price has been calculated putting the quantity on the inverse
demand function.
The general formula for the revenue is = Quantity* Price
The formula for the cost = 23*q1
The general formula for the profit of the firm 1= (100-q1d-q2d)q1d-23q1d
The general formula for the profit of the firm 1= (100-q1d-q2d)q2d-23q2d
b. The general calculations of profit has matched with the profit calculated in the part a.
Both the firms in this case are earning a profit of 658.77.
The general formula for the calculations of the profit in this case is Total revenue-
Total cost.
Question 3
a. The general formula for the merged firm is= q1= (77-q2d-q2u)/2
This is then put in the inverse demand curve where the industry price is got.
The general formula for the profit for the merged firm is= (100-q1d-q2d-q2u)*q1d-
23*q1d

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b. The general formula for the downstream firm is = (100-q1d-q2u-p2u)/2
Where, p2u= the upstream price charged
The general formula for the upstream firm is= (100-q1d-q2d)/2
The general profit function for the downstream firm = (100-q1d-q2d-q2u)*q2d-23*q2d-
p2u*q2d
The general profit function for the upstream firm= (100-q1d-q2d-q2u)*q2u-23*q2u
c. The general formula for profit is equal to the one calculated in the first and the second
part of this question.
The profit for the merged firm in this case is 639.36. The profit for the downstream
firm is -26.28 and the same for the upstream firm is 668.26.
The general formula for the calculations of the profit is the difference between the
Total revenue- Total costs.
Question 4
The vertical merger is defined as a situation where the manufacturer and the supplier merge
in order to make a single organisation. One of the biggest advantages of the vertical merger is
that it reduces the cost of operation of the organisation and hence the profit margin increases
(Slade and Margaret 2020). This paper deals with different models where organisations are
not merged, merged and partially merged. The result of this study finds out that, only one
vertical merger in the market can reduce the profit margin of the downstream firm increasing
the profit of the upstream for more than a merged firm (Chen et al. 2017). Therefore in the
long run the downstream firm will exit the market leading to a void in the supply chain.
Therefore there is not rationality in one vertical merger in a cournot model.
The paper also deals with a problem where there are no mergers in the market and hence the
upstream and the downstream firms are separate from each other. The results that have been
found from the analysis that the downstream firms will always lose in these settings as the
highest benefits will be enjoyed by the upstream firms (Salop et al. 2020). The profit of the
downstream firms in this case is very low compared to the other forms and hence there is no
rationality for the downstream firm to stay in the market. It needs to be noted that the profit
for the upstream firms of the market is also low in this case as the cost of the production
increases the price and hence the demand for the product reduces.

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Therefore the vertical merger that has been shown in the analysis is the parreto optimum
solution for the Cournot duopoly model (Rogerson and William 2020). The vertical merger
between the downstream and the upstream firm in this case will reduce the cost of the
production and hence the prices of the product will remain low leading to a higher demand.
Apart from that the two vertical mergers of the firms in the market also maximises the profit
of the individual firms as well. It needs to be noted that the industry price for this model is the
lowest among all the cases that has been studied in this paper. Therefore the consumer
surplus is also high that means this model of vertical merger is socially efficient given the
presence of only two firms in the market (Domnenko et al. 2019). However, in the case of
two vertical mergers the production of the products will also reduce owing to the low market
price for the product. Therefore, two vertical mergers is the optimum case in the duopoly
model of Cournot where the market prices of the goods or the services are lower and the
profit is the highest. The consumer surplus is also higher compared to the other models and
hence more efficient.

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Reference
Chen, Pengyu, He Xu, and Xuxia Zou. "The effects and incentive of vertical mergers: An
analysis from the view of OM." European Journal of Operational Research 263.1
(2017): 158-172.
Domnenko, Gleb B., and David S. Sibley. "Simulating Vertical Mergers and the Vertical
GUPPI Approach." Available at SSRN 3447687 (2019).
Rogerson, William P. "Modelling and Predicting the Competitive Effects of Vertical
Mergers: The Bargaining Leverage Over Rivals (BLR) Effect." (2020).
Salop, Steven C., and Serge Moresi. "Quantifying the Increase in “Effective Concentration”
from Vertical Mergers that Raise Input Foreclosure Concerns: Comment on the Draft
Vertical Merger Guidelines." Available at SSRN (2020).
Slade, Margaret E. Vertical Mergers: Ex Post Evidence and Ex Ante Evaluation Methods.
No. margaret_e. _slade-2019-10. Vancouver School of Economics, 2019.