7. The director of a theater company in a small college town is considering changing the way he prices tickets. He has hired an economic consulting firm to estimate the demand for tickets. The firm has classified people who go to the theater into two groups and has come up with two demand functions. The demand curves for the general public (Qgp) and students (Qs) are given below:
Qgp=500 - 5P
Qs = 200 - 4P
a Graph the two demand curves on one graph, with P on the vertical axis and Q on the horizontal axis. If the current price of tickets is $35, identify the quan tity demanded by each group.
b. Find the price elasticity of demand for each group at the current price and quantity.
c. Is the director maximizing the revenue he collects from ticket sales by charging $35 for each ticket?
What price should he charge each group if he wants
to maximize revenue collected from ticket sales?
Find price elasticity of demand.
1)For each of the following cases, calculate the arc price elasticity of demand and state whether demand is elastic, inelastic or unit elastic
a) when the price of milk increases from $2.25 to $2.50 per gallon, the quantity demanded falls from 100 gallons to 90 gallons
b) when price of paper book falls from $7.00 to $6.50, quantity demanded rises from 100 to 150
c) when the rent on apartments rises from $500 to $550, the quantity demanded decreases from 1000 to 950 2)
2. For each of the following cases, calculate the point price elasticity of demand and state whether demand is elastic, inelastic or unit elastic. The demand curve is given by
a) The price of product is $50
b) The price of product is $75
c) The price of product is $25
3. For each of the following cases, what is the expected impact on the total revenue of the firm. Explain your answer
a) Price elasticity of the demand is known to be -0.5, and the firm raises the price by 10%
b) Price elasticity of the demand is known to be -2.5, and the firm lowers the prices by 5%
c) Price elasticity of the demand is known to be 1, and the firm raises the prices by 1%
d) Price elasticity of the demand is known to be 0, and the firm raises the prices by 50%
4.The demand curve is given by
a) What is the total revenue function
b) The marginal revenue function is MR=250-Q
Graph the total revenue function, Demand curve and marginal revenue function c) c) At what price is revenue is maximised, What is the revnue at that point
d) Identify the elastic and inelastic portions of demand curve