Chapter 2.7, Problem 11E

Demand for oil. Suppose you have been hired as an economic consultant concerning the world demand for oil. The demand function is

$q=D\left(x\right)=50,000+300x-3x^2,\text{for}0\le x\le 180,$

Where q is measured in millions of barrels of oil per day at a price of x dollars per barrel

a. Find the elasticity

$E\left(x\right)=\frac{6x^2-300x}{50,000+300x-3x^2}$

b. Find the elasticity at a price of $75 per barrel, stating whether demand is elastic or inelastic at that price

c. Find the elasticity at a price of $100 per barrel stating whether demand is elastic or inelastic at that price

d. Find the elasticity at a price of $20 per barrel, stating whether demand is elastic or inelastic at that price

e. At what price is revenue a maximum?

f. What quantity of oil will be sold at the price that maximizes revenue? Compare the current world price to your answer

g. At a price of $110 per barrel, will a small increase in price cause total revenue to increase or decrease?