Question

Firms A and B are in a market of fixed size (Size = 1), developing a product for their customers. The more R and D they undertake i.e. the more time they spend, the better product they are able to launch in the market. However, the firms are facing a constraint; whoever launches their product first, will gain a market share of customers that cannot be transferred to their opponent. In this case the opponent will obtain the remainder of the customers in the market. If both A and B launch their product at the same time, the share of customers will be equally divided amongst them. Each firm has to choose time t at which they will launch their product in the market. The share of customers in the market is defined by the function f(t)=t where f(0)=0 and f(1)=1 (The share of customers in the market is a function that increases over time with the lowest share being 0 and the maximum share of customers equal to 1). Assume time and hence market share of customers is perfectly divisible over the spectrum of time defined as t = {0..............1}. Hint: This means that any fractional amount of time and hence market share is possible 1/3,1/4, 1/6 etc,

Kindly post the steps in detail

Answer 1

As mentioned in the question

keeping other firms being constant two firms( i.e.A&B)

are fighting for maximum market share of customers for their product launch.

As pper the question whomever will luanch the product first will get the maximum share

considering function f(t) = t where t is time ranges {0....1} and f(0)=0 & f(1)= 1.

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In this graph the relation is positive according to function f(t)=t

for example: firm A launches product at 1/6th time then market share of firm B will be 1/6th and remaning market share will be of firm A

for maximum share they had to bid for time along with others constraints like prereceived cost and pre received benefits

and for better results firm with majority of votes and availability of funds should launch at 2/6th of time so that share could be balanced

and if they think like rivals then bidding for time is the option

and keeping other constraints in favourable.