Suppose that a price setting firm has the following direct demand function:
Qd = 100-20P
- Find the inverse demand curve. What is it's slope and its intercept?
- Find the equation for Total Revenue.
- Find the equation for Marginal Revenue.
- What is the quantity where Total Revenue is maximized? How is this related to Marginal Revenue?
- Calculate the own price elasticity of demand at the quantity where Total Revenue is maximized.
- A decrease in price below $2.00 will do what to Total Revenue? To Marginal Revenue? Why? Hint: Drawing the two graphs (the one with D and MR drawn against Q and the second with TR drawn against Q might help.
- Suppose now that the firm is a profit maximizing firm, and that MC = 2.5 + .025Q. Find the profit maximizing output and price. Calculate the own price elasticity of demand at the profit maximizing price and output.
- Given your results, is there a difference between maximizing Revenue (part d) and maximizing profits (part g). Why?