# value of the own-price elasticity of demand

Please show all work and calculations.

Consider a monopoly firm facing market demand expressed as p = 200 - ½y , where the firm's total cost in dollars per month is: TC = 2y2 + 15y + 144, where p is measured in dollars per unit and y is measured in units per month.

a. Write the expressions for the firm's Total Revenue, Marginal Revenue, Average Cost and Marginal Cost.

b. Show on a graph, supported by calculations, what quantity this monopolist will produce each period to maximize profits. Your graph should also show (and label) the demand curve, marginal revenue curve and marginal cost curve. Report the firm's optimal price per unit.

c. Calculate, and label as point A on your graph, the value of average cost at the optimal output level.

d. Calculate the firm's profit per month and show it as a shaded area on your graph.

e. What is the value of the own-price elasticity of demand at the profit maximizing quantity?

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#### Solution Summary

The value of the own-price elasticity of demand is derived.

Strategic Management

B.B. Lean is a catalog retailer of a wide variety of sporting goods and recreational products. Although the market response to the company's spring catalog was generally good, sales of B.B. Lean's $140 deluxe garment declines from 10,000 to 4,800 units. During this period, a competitor offered a whopping $52 off their regular $137 price on deluxe garment bags.

a) Calculate the arc cross-price elasticity of demand for B.B. Lean's deluxe garment bag.

b) B.B. Lean's deluxe garment bag sales recovered from 4800 units to 6000 units following a price reduction of $130 per unit. Calculate B.B. Lean's arc price elasticity of demand for this product.

c) Assuming the same are price elasticity of demand calculated in part B, determine the future price reduction necessary for B.B. Lean to fully recover lost sales (i.e., regain a volume of 10000 units).