Question

Suppose you come home from having earned your degree at CSUEB. Your parents own a local chain of fitness clubs that have a great reputation. Your father uses cost-plus pricing, and at the moment he is charging $200 for an annual membership, and is currently selling 800 memberships. Your parents are quite happy with their current markup above average costs You suspect that perhaps they could be doing better and be more profitable. As you just took ECON 380, you are well equipped to assess this! After consulting with the club's manager, you learn that the cost function for annual memberships is given by c(Q)=1000+20Q+(1/20)Q². Further, they tell you that the own price elasticity of demand is approximately -2.5 Are your parents choosing a membership price that is maximizing profit? If not, what would you suggest - increase the price or reduce the price? Explain.

Answer 1

To maximize profits for the fitness club with an own price elasticity of -2.5, a price reduction is suggested, as the demand is elastic. For a pharmaceutical company with an own price elasticity of 1.4, lowering the drug's price is recommended to increase revenue; with 0.6 elasticity, an increase is advised, and at an elasticity of 1, maintaining the current price is optimal.

Step-by-step explanation:

The question involves assessing whether a fitness club is pricing its annual memberships to maximize profits, given an own price elasticity of demand of -2.5 and a cost function. When the absolute value of price elasticity of demand is greater than 1, it indicates that the quantity demanded is highly responsive to price changes (elastic demand). Since the elasticity is -2.5, the demand is elastic, and therefore, lowering the price should result in a more than proportional increase in the number of memberships sold, potentially increasing total revenue. If the elasticity were less than 1, it would suggest that demand is inelastic, and raising the price could lead to higher total revenue.

For the pharmaceutical company's question, if the own price elasticity of demand for the new hair growth drug is 1.4, the company should reduce the price to maximize revenue because a price decrease will lead to a proportionally larger increase in quantity demanded. If the elasticity were 0.6, the demand is inelastic, and the company should increase the price to maximize revenue. If the elasticity is exactly 1, then the company is already maximizing revenue, and no price change is necessary.

Lastly, the gasoline price elasticity of supply is important for companies like UPS or FedEx as it indicates how responsive the quantity of gasoline supplied is to price changes, which can affect their operational costs for shipping and delivery services.