Here are some problems one might face while working for a marketing agency:
Assume that the demand function for women's basketball tickets is as follows:
Qd = 20,000 - 2000P
1) Graph the demand curve, and give some verbal interpretation. Compute the intercept and slope of the demand curve.
2) Use the point elasticity formula to calculate the point elasticity at the price of $4.00. Give a verbal interpretation of this elasticity. Is the elasticity considered "elastic" or "inelastic"?
3) Using the elasticity you just computed, what would happen to attendance if the price were to be reduced by 7%? By what percentage will ticket sales change? Would this increase or decrease total revenue?
4) Noting that the slope of the demand curve is constant, calculate the elasticities at the prices $8, $7, $6, $5, $4, $3, and $2. Which of these points are elastic? Which of these points are inelastic? Show on the curve, the elastic and inelastic regions and the point of unit elasticity. Calculate the total revenue at each different price level. At which price level is total revenue maximized? Make a table to present your results, including prices, quantities, elasticities, and total revenues.
5) Assume that the income elasticity of demand for tickets is +2.5. Also assume that the average household in the community makes $20,000 per year and that about 6000 tickets are sold per year. Now let the average household income go up to about $22,000 per year. Now how many tickets do you expect to be sold in a year?
6) In addition to basketball games, there is also the possibility of attending ice hockey games, for which tickets are $8.00. Assuming a cross-price elasticity (percentage change in demand for basketball tickets per percentage change in hockey ticket prices) of +1.5, what will happen to attendance at basketball games if hockey tickets rise to $10.00 per ticket? By how much will there be the rise/fall in attendance at basketball games? Are hockey games a substitute for basketball games or a complement? Why?
7) Let the demand function for basketball tickets be as follows:
Qd = 40,000/P
(a) What is the arc elasticity of demand between $4.00 and at $5.00?
(b) What is the point elasticity of demand at $4.00 and at $5.00?