Managerial Economics
Market Demand 200 X 200 (x1x2x3)
Marginal Cost 40 for each firm
Break the Equations in such a way that we separate quantity of any one firm and do our workings accordingly. Hence,
P 200 x1 2Y (Where 2Y x2x3)
To maximize Profit of x1 the equation will be
(200 x1 2Y) x1 40x1
200x1 x12 2Yx1 40x1
160x1 x12 2Yx1
Now Find Derivative of the above equation and equate to 0
DP Dx1 160 - 2x1 2Y 0
) 2x1 160 - 2Y
) x1 80 Y
As x1 is identical to x2 and x3
) x1 Y 80 Y
As, Y Y 80
) 2Y 80
) Y 40
For Industry 403 120
Quantity
x1 40
x2 40
x3 40
Price 200 (403)
Price 200 120
Price 80
For Profits
1 (Price Marginal Cost)x1
1 (80 40)40
1 4040
1 1600
As 1 2 3
Profits
1 1600
2 1600
3 1600
Over all Profits 16003 4800
PART B
We have seen the pre merger situation in part (a)
Now if we merge Firm 1 and 2 then,
The Inverse Demand Function is
P 200 X, where X (x1 x2 x3)
And Marginal Cost is 40
The combined profit after merger equals the profit of the merged firms A
) A (200 X) xA 40 xA
Firm A s output, xA, equals x1 x2. Since marginal costs of both firms are constant, 40, firm A if indifferent about where its output is produced. After they are merged x1 and x2 are Indeterminate though their Sum is Determinate.
The First Order Condition for Profit-maximizations (FOC) of the two firms in the industry after the merger (firm A and the other firm)
The Best Response function in a Cournot competitor
) 200 X3 x3 40
) 200 XA xA 40
The mergers give rise to a number of effects which, for purpose of expositions, we sometimes describe as it occurring sequentially even though they come up simultaneously.
) Firm 3s FOC after the merger equation implies that dx3 dxA - 0.5
) Firm As FOC implies that dxA dx3 - 0.5
Working will be done through firm As equation
) Max (xA) (200 XA xA) xA 40xA
Now after differentiating the above equation
) 200 XA 2xA 40 0
) 160 X xA
) 160 X (XN), (Where N Number of firms in the industry and in this case N 2, Industry A and Industry 3)
) 160 X (X2)
) 160 1.5X
) X 1601.5
) X 106.67
By putting X 106.67 in the equation
) 200 xA 106.67 40
) xA 53.33
As X xA x3
) 106.67 53.33 x3
) x3 53.33
) A (200 XA) xA 40 xA
) A (200 106.67)53.33 40(53.33)
) A 2844(Approx)
We can notice that A 2844 is clearly LOWER than the sum of x1 x2 in part (a) that is 1600 1600 3200, hence it proves that the merge of Firm 1 and Firm 2 is Unprofitable.
PART C
The Inverse Demand Function is
P 200 X, where X (x1 x2 x3)
And Marginal Cost is 20
The combined profit after merger equals the profit of the merged firms A
) A (200 X) xA 20 xA
Firm A s output, xA, equals x1 x2. Since marginal costs of both firms are constant, 40, firm A if indifferent about where its output is produced. After they are merged x1 and x2 are Indeterminate though their Sum is Determinate.
The First Order Condition for Profit-maximizations (FOC) of the two firms in the industry after the merger (firm A and the other firm)
) 200 X3 x3 20
) 200 XA xA 20
The mergers give rise to a number of effects which, for purpose of expositions, we sometimes describe as it occurring sequentially even though they come up simultaneously.
) Firm 3s FOC after the merger equation implies that dx3 dxA - 0.5
) Firm A s FOC implies that dxA dx3 - 0.5
Working will be done through firm A s equation
) Max (xA) 200 XA xA) xA 20xA
Now after differentiating the above equation
) 200 XA 2xA 20 0
) 180 X xA
) 180 X (XN), (Where N Number of firms in the industry and in this case N 2, Industry A and Industry 3)
) 180 X (X2)
) 180 1.5X
) X 1801.5
) X 120
By putting X 120 in the equation
) 200 xA 120 20
) xA 60
As X xA x3
) 120 60 x3
) x3 60
) A (200 XA) xA 20 xA
) A (200 120)60 20(60)
) A 3600
Now we can clearly see the impact of the change of Costs in the merge has positively affected the profitability of the firm which has Now Increased from 2800 in (b) to 3600 in part (c) which is Greater than the pre merger profits that was 3200. Hence Proved
PART D
Though we can see that the merge in part (b) proved to be unprofitable and the output of Firm A was 53.33 as compared to the individual outputs before the merger took place between that was (40 40 80). Outputs are one of the important aspects of profits, the more output a firm produces the more profits a firm will earn considering the costs as well. But the quantity of output matters with the quality and not only that but all of it depends on the demand of that product which is a consumer want and accordingly producers have to respond with their output quantity to gain recognition in the market. Secondly the market price that was 80(200 120) in part (a) actually increased to 93.33(200 106.66) It might be due to NO changes in the costs of their firm and an aim to increase their profits in order to meet the point of profits that were being earned before the merge. Mergers usually take place to decrease the costs and increase the profitability to gain market share and play monopoly that is to kick the small other competitors out of the market but in this case i.e. part (b) it turned out to be adverse as Firm 3 took clear advantage of it and increased its profitability to 2844 (approx) from 1600 before any mergers. Firm 3 were able to produce more output after the firms 1 2 merged as a result they increased their profitability with the same number of costs incurred as before. Hence merge in567