Consider the linear demand function Q = 20 – 0.5P.
a. Write the inverse demand function.
b. Write the total revenue function.
c. Using calculus, find the level of output, Qrmax, where total revenue reaches its maximum value. What price Prmax maximizes total revenue? What is the value of TR at its maximum point?
d. Write the equation for marginal revenue. Using MR, verify that Qrmax derived in part c maximizes total revenue.
e. Calculate the point elasticity of demand at Prmax. Does E have the expected value? Explain briefly.