The Zinger Company manufactures and sells a line of sewing machines. Monthly demand for one its most popular models is given by the following relationship:
Q = 400 - 0.5P
where P is price and Q is quantity demanded. Total costs of production (including a "normal" return on owners' investment) per month are:
C = 20,000 + 50Q + 3Q2
a. Express total profits in terms of Q.
b. At what level of output are total profits maximized? What price will be charged? What are total profits at this output level?
c. What market structure did you assume? Why?
d. Would your answers in b change if the market for sewing machines were competitive? How? (Specify price, quantity, and profit levels.)