Question

(Inspired by the events in the Montreal cement market in 1966.) You are the CEO of Independent Cement (IC), and are considering whether and how to enter the Montreal market. If you enter, you must first choose whether to build a small plant that can serve up to 100 customers, or a large plant that can serve all 400 customers in the Montreal metropolitan area; in either case, the cost of the plant is $300 and the marginal cost of producing one unit of cement is $3.

Answer 1

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