Optimization: In this assignment, we use Excel's problem solutions to solve a profit maximization problem for a company with monopoly power. The goal for the company is to choose the production level that maximizes the difference between income and costs (maximizes profit). The monopolist takes as given the demand in the market and production costs: Demand: The relationship between price and quantity demanded can be described by the function = ()= 100 - where denotes quantity demanded and denotes the price that the monopolist chooses. Costs: The monopolist has costs that are quadratic with the production level: () = 2. Read the following problems in a spreadsheet:

a. Use an Excel formula to calculate the quantity demanded for each price between 0 and 100. Put the price in column A and calculate the quantity demanded in column B. In addition, create a diagram showing the relationship between demand and price (scatter diagram with smoothed lines is a good choice). What happens to the quantity demanded when the price is fixed?

b. Use the result from part a to calculate the income/turnover for each production level. Remember that turnover is price multiplied by the number of units sold. Show the relationship between income and quantity demanded in a diagram. Give an intuitive explanation for why the relationship?