What are the profit-maximizing price and output levels?

Problem 1: 

Robert’s New Way Vacuum Cleaner Company is a newly started small business that produces vacuum cleaners and belongs to a monopolistically competitive market. Its demand curve for the product is expressed as Q = 5000 – 25P where Q is the number of vacuum cleaners per year and P is in dollars. Cost estimation processes have determined that the firm’s cost function is represented by TC = 1500 + 20Q + 0.02Q2.

Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary.

  1. What are the profit-maximizing price and output levels? Explain them and calculate algebraically for equilibrium P (price) and Q (output). Then, plot the MC (marginal cost), D (demand), and MR (marginal revenue) curves graphically and illustrate the equilibrium point.
  2. How much economic profit do you expect that Robert’s company will make in the first year?
  3. Do you expect this economic profit level to continue in subsequent years? Why or why not?