Suppose that the quantity demanded is a linear function of price, and it has a negative slope. Average cost is a
constant cost function. Profit equals total revenue minus total cost.
(a) Give algebraic expressions for quantity demanded and for average cost.
(b) Find expressions for average revenue and total revenue as a function of quantity, and sketch the graphs of both. Find a quantity where total revenue is at a maximum.
(c) Find expressions for total cost as a function of quantity. Sketch the total cost function into the graph with total revenue.
(d) Find expressions for profit as a function of quantity. What is its functional form? Sketch the profit function to total revenue and total cost functions.