Question: Demand Elasticity and Profit Maximization

A consumer marketing firm has been test marketing a new product in a number of markets. This firm believes that demand for its product comes entirely from women aged 15 to 35, and that demand is quite different for different age groups in this range. It is unrealistic to assume that the firm knows the full demand function that it faces for each of the segments in the market. What is much more realistic to assume is that the firm knows "local" data about the demand by various segments, local in the sense that the data will be for small changes in price only. For example, the firm might know, on the basis of consumers surveys or test marketing, that at the price of $8:

Per 1000 women aged 15 to 20, it can expect to sell 600 units of the good, with a price elasticity of –1.0;

Per 1000 women aged 21 to 25, it can expect to sell 500 units of the good, with a price elasticity of –1.2;

Per 1000 women aged 26 to 30, it can expect to sell 600 units of the good, with a price elasticity of –1.5, and

Per 1000 women aged 31 to 35, it can expect to sell 300 units of the good, with a price elasticity of –2.0.

Please answer the following questions:

1. In a market with 25,000 women aged 15 to 20, 15,000 aged 21 to 25, 10,000 aged
   26 to 30, and 5000 aged 31 to 35, how many units can the firm expect to sell at a
   price of $8 per unit? Approximately how many can it expect to sell at a price of
   $8.16?
2. Suppose the firm has a constant marginal cost of production of MC = $2 per unit. Is the price of $8 per unit too high, too low, or just right for profit maximization, based on the data given in part (a)?

Price: $2.99

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