A firm currently has a 20% market share for its product, lint pickers. It has identified 2 plans to improve its market share. The transition matrices for both plans are listed below. Plan 1 costs $1 million and Plan 2 costs $1.5 million
The company's goal is to determine what its demand will be in the long-term.
Plan 1: 20% Share 40% Share 60% Share
20 Share 0.25 0.40 0.35
40 Share 0.20 0.35 0.45
60 Share 0.10 0.50 0.40
Plan 2: 20% Share 40% Share 60% Share
20 Share 0.30 0.30 0.40
40 Share 0.10 0.50 0.40
60 Share 0.20 0.30 0.50
A single percentage point of market share translates into an annual demand of 1,000 units per year. Also, each percentage point of market share means $100,000 of profit for the firm. Choose the plan that maximizes the firm's net income.
Plan 1 has the highest net income. Average market share in plan 1 is 44.91139 and for plan 2 it is 45.27778. The additional income of plan 2 is not enough to compensate for the marginal increase in cost.
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