Question

3) Suppose a firm sells to senior citizens and others at a single price of $10. At this price it sells 20,000 units total (4,000 to seniors; 16,000 to others). It estimates that at the $10 price, seniors have an elasticity of -3 while others have an elasticity of -1.5.

a) How could this firm change its pricing strategy to increase profits while holding its overall level of production constant and continuing to use only linear (per unit) prices? Be specific, and show that your suggestion works by calculating the change in profits from your suggestion.

Answer 1

There is currently a single price of $10. At this price it sells 20,000 units total (4,000 to seniors; 16,000 to others). It estimates that at the $10 price, seniors have an elasticity of -3 while others have an elasticity of -1.5.

We know that price elasticity = slope x P/Q

For seniors we have -3 = slope x 10/4000. This gives slope of demand function for seniors = -1200. Demand function is Q = A - PB or 4000 = A - 10*1200 which gives A = 16000. Hence demand function for seniors is given by Qd = 16000 - 1200Ps

For others we have -1.5 = slope x 10/16000. This gives slope of demand function for others = -2400. Demand function is Q = A - PB or 16000 = A - 10*2400 which gives A = 40000. Hence demand function for others is given by Qd = 40000 - 2400Po

Current profits are (with zero cost) = 10*20000 = $200000

Total production is fixed at 20000

16000 - 1200Ps + 40000 - 2400Po = 20000

1200Ps + 2400Po = 36000

Ps + 2Po = 30

Now using this we find that if Ps is reduced to 8, Po becomes 11 and then profit becomes 8*(16000 - 8*1200) + 11*(40000 - 2400*11) = $200800. See that by charging different prices, the monopolist can increase her profits.