DUOPOLY MODELS the market demand for pair of duoplisti is given by P= 36-3Q where Q=q1+q2. for each duoplist the constant per unit marginal cost is $18/unit and fixed cost are zero (1) find the equilibrium market price and the equilibrium quantites and profits for cournot duoplist. (2) find the equilibrium market price and the equilibrium quantity and profit for each firm assuming that the firm act as stackelberg leader and cournot follower with firm 1 as leader (3) find equilibrium price and the equilibrium quantities and profit for bertrand duopolists (4) find the equilibrium market price and the equilibrium quantities and profits for firms acting as duopolistic (equally sharing) cartal. (5) using well labelled digrams compare the results for the four duopoly models in (1)-(4) in terms of market price and quantity the equilibrium quantity or each firm and the profits for each firm. note (the comparison requir three diagrams for the overall market the duoplists best respons or reaction function curves and the profit possibilities) Solution 1. Inverse demand function is P = 36-3(q1+q2) Total cost function of both the firms is C1 = 18q1 and C2 = 18q2 MC = 18 for both the firms. To find firm 1.

1. DuPont Identity)
1)Using the DuPont Identity equation, compare your company's 2014 ROE with competitor's
2014 ROE. Find out what makes difference in ROEs between your company and competitor.
2)Using the DuPont Identity equation, compare your company's 2013 ROE with 2014 ROE.
Find out what makes difference in ROEs between two periods if there is any difference.
5.Using the dividend payout ratios of your company and competitor, compute the internal growth
rates and sustainable growth rates for both companies and compare each other.
Per Finance.yahoo.com
Return on Assets Ratio = Net Income/ Total Average Assets, where total average assets =
(Assets in the beginning+ assets in the end)
For PWS for year 2014,
Net Income = 1,26,516
Total Average Assets = (3,376,436+3,392,570)/2 = 3384503
Hence Return to Asset Ratio = 126516/3384503 = 0.037
For CWS, for year 2014,
Net Income = (27,404)
Total Average Assets = (649,897+663,119)/2 = 656508
ROA= - 0.041
PWS Income Statement and Balance Sheet
94,357
55,620
CWS Inome and Balance Sheet
(88,245)
(77,586)Direct Competitor Comparison
Solution
Return on equity(ROE)= Net profit/Average Equity
Net profit (NP)=Net profit/Sales
Asset turnover Ratio(ATR)=sales/Average total assets
Equity MultiplierEM)=Average Total Assets/Average Equity
Net profit/Average Equity=(Net profit/Sales)*(sales/Average total assets)*(Average Total
Assets/Average Equity)
Assuming PWS as my company and CWS as my competitor

2. For PWS ROE for 2014
Net Profit=126,516
Sales=2,008,997
Average total assets=(3,376,436+3,392,570)/2=3,384,503
Average Equity=(1,228,793+1,289,571)/2=1,259,182
ROE=(126,516/2,008,997)*(2,008,997/3,384,503)*(3,384,503/1,259,182)*100
=(0.063)*(0.594)*(2.688)=10.04%
For CWS ROE for 2014
Net Profit=(23,095)
Sales=497,633
Average total assets=(649,897+663,119)/2=656,508
Average Equity=(-8407+11285)/2=1,439
ROE=(-23,095/497,633)*(497,633/656,508)*(656,508/1,439)*100
=(-0.0464)*(0.758)*(456.225)=-1605%
If we see overall ROE for PWS it is 10% and for CWS it is -1605% which is very very bad . The
net profit is negative for CWS because they have positive operating income but because of huge
debt there net income is negative