1. Consider the linear demand function Q=320-1/8P
a. Write the inverse demand function.
b. Write the Total revenue function.
c. Find the level of Q, where total revenue is maximized. Find the price, P that maximizes TR. What is the value of TR evaluated at the critical values, (Qmaximum, Pmaximum)?
2. You are manager at an athletic club, and you must determine the best price to charge for locker rentals. Assume the marginal cost of providing lockers is zero. The monthly demand for lockers is determined to be: Q=3000-350P where P is the monthly rental price and Q is the number of lockers demanded per month.
a. What price would you charge to maximize revenue?
b. What is the TR revenue function?
c. Find the level of Q, where total revenue is maximized. Find the price, P that maximizes TR. What is the value of TR evaluated at the critical values, (Qmaximum, Pmaximum)?
3. a. When demand is inelastic, an increase in price causes quantity demanded to ____ and TR to ____.
b. When demand is elastic, a decrease in price causes quantity demanded to ____ and TR to ____.
c. When demand is unitary elastic, an increase in price causes quantity demanded to ___ and TR to ____.
d. If price falls and total revenue stays the same, demand must be _____.
e. If price rises, and total revenue falls, demand must be _____.
4. Find the first derivative for the inverse of each of the following functions.
a. Q=-3P+652
b. P= 280-2/3Q
5. Given the demand function P=108-3Q,
a. Find the marginal revenue function.
b. Find the average function.
c. Find the total revenue function.
6. The price elasticity of demand for imported tequila is estimated to be -0.20 over a wide interval of prices. The federal government decides to raise import tariffs on foreign booze, causing the price to rise by 20%. Will tequila sales rise, fall, or stay the same, and by what percentage amount?