Answer:
1) C.C. is currently selling at $ 12. So, if I.C.'s price is equal to C.C.'s it can sell to all the 400 customers. Hence, IC should keep the price at $12. The CC's price after price determination by IC will be $ 11 as doing so, CC will be able to sell to all 400 customers. Expected profits of IC will be as follows:
Sales =12 *400
Less : Marginal cost = 3*400
Expected profits = $ 3600
(2) If IC builds a small plant, then it can sell upto its capacity i.e. 100 units to 100 customers, if its price is no greater than IC. So IC can keep its price at $ 12. Expected profits of IC = 100 *12 less marginal cost i.e. 3*100 = $ 900.
As a result of above, CC will keep its price either 11 or 12.
Case 1( If CC's price is 11)
Expected profits = sales- marginal cost = 400* 11 - Marginal cost i.e. 4 * 400= 2800
Case 2 ( If CC's price is 12)
Expected profits = sales- marginal cost = 300* 12- Marginal cost i.e. 4* 300 =2400
So, CC's price would be $ 11 as it leads to maximisation of his profits
(3) The choice of size of plant will be dependent upon the profits and is driven by profit maximisation factor.
Case 1 ( If small plant is chosen)
Sales = 100 * 12
Less : Marginal cost = 100 * 3
Profits = $ 900
Case 2 ( If large plant is chosen, we should keep our price at 11 as CC would always keep the price at 11 , not 12 as it maximises its profit at 11)
Sales = 400 * 11
Less marginal cost : 3 * 400
Profits = 3200
Hence, large plant should be chosen
