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For most products, higher prices result in a decreased demand, whereas lower prices result in an increased demand (economists refer to such products as normal goods). Let
d = annual demand for a product in units
p = price per unit
Assume that a firm accepts the following price–demand relationship as being a realistic representation of its market:
d = 800 10p
where p must be between $20 and $70.
a. How many units can the firm sell at the $20 per-unit price? At the $70 per-unit price?
b. What happens to annual units demanded for the product if the firm increases the per unit price from $26 to $27? From $42 to $43? From $68 to $69? What is the suggested relationship between per-unit price and annual demand for the product in units?
c. Show the mathematical model for the total revenue (TR), which is the annual demand multiplied by the unit price.
d. Based on other considerations, the firm’s management will only consider price alternatives of $30, $40, and $50. Use your model from part (b) to determine the price alternative that will maximize the total revenue.
e. What are the expected annual demand and the total revenue according to your recommended price? |
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