1. You are in charge of managing a small group of rental car offices. Some customers are Costco and/or AAA members ("cardholders"), and these customers have been getting a discount on the weekly rate for the economy cars that you rent. At present, 100 customers per week rent cars and get the discount, and another 100 customers per week rent cars without getting a discount. These numbers are not expected to change for the time being.
There has been a debate inside the company about whether there should be a charge for mileage driven during the week. The estimated wear and tear on the vehicles (depreciation) is $1.00 per mile driven, and the company has had a mileage charge of this amount (the marginal cost of driving) for all vehicles rented. Some people believe that there should not be any mileage charge at all. A few people believe the mileage charge should be $1.50 per mile.
Based on past experience, the demand curves for the miles driven by a typical cardholder and the miles driven by a typical non-cardholder can each be approximated by a straight line. For the cardholders, the estimate is that, if there were no mileage charge, a cardholding renter would typically drive 800 miles during a one week rental. For non-cardholders the estimate is 450 miles. For cardholders, if the mileage charge reached $2.00 per mile, no cardholder would want to drive any miles. For non-cardholders, the mileage charge would have to reach $3.00 per mile for the quantity demanded to fall to zero.
Draw a demand curve for a typical cardholder for miles to be driven during one week, and do the same for a typical non-cardholder. For the three different mileage charges under consideration--$0.00, $1.00, and $1.50-determine the maximum weekly rental charge that could be assessed without a typical cardholding customer dropping out of the market. Do the same for a typical non-cardholding customer.
For the time being, which of the mileage charges, when combined with a weekly rental rate, would be best for the company? Would it still be wise to offer a discount for the cardholders? What would be the weekly rental rate for a cardholder, and what would be the weekly rental rate for a non-cardholder?
Show all your work. Remember that the area of a triangle is ½ x the base x the height.
2. You have the responsibility for establishing the pricing for a product to be released in three stages. A different and cheaper version of the product will be sold at the 2nd and 3rdstages. If the marginal cost of production is 50 percent lower for the second stage, and it is another 50 percent lower for the third stage, discuss the optimal pricing for the company in a case where the price elasticity of demand is twice as high for the second stage (as compared to the first stage), and the elasticity for the third stage is twice as high as it was for the second stage. Construct a numerical example and offer a conclusion about optimal pricing for the three stages. Show all your work.
3. The firms in a perfectly competitive industry had been earning zero economic profits. However, the firms have recently experienced a large decrease in the cost of energy that enables them to substantially reduce the marginal cost and average total cost of producing each unit of output. The market demand for the product is pretty elastic. On the other hand, short-run efforts to increase production run into severely diminishing returns with respect to the employment of additional variable inputs.
Draw two average total cost curves (ATC) for a typical firm. One curve should represent ATC before the fall in the cost of energy. The other curve should represent ATC after the fall in the cost of energy. Assume that the fall in the cost of energy does not affect the minimum efficient scale (MES) of production. Draw short-run marginal cost curves on the same diagram to show both the fall in the cost of energy and the severely diminishing returns to the employment of additional variable inputs.
Next to the diagram for a typical firm, draw a supply-demand diagram for the industry. The slope of the demand curve should reflect the elasticity of demand for the product. The short-run supply curve should reflect the presence of severely diminishing returns with respect to the employment of additional variable inputs. The original equilibrium price in this diagram should line up with the minimum point of the original ATC curve for a typical firm.
Properly shift demand or supply to reflect the fall in the cost of energy. Note the change in the market equilibrium. How does the magnitude of the change in the market price compare to the magnitude of the shift in ATC? Explain. Do firms now experience short-run economic profits? In the long-run, can entry of new firms be expected in this industry? If we have a decreasing cost industry, show in your diagrams where the cost curves, the market price, and the equilibrium market quantity end up. Fully explain what has happened. Does the equilibrium quantity end up changing much in comparison to the magnitude of the overall change in price? Why or why not?
4. A central city imposes a rent control law that places a binding ceiling on the rent that can be charged for an apartment. The suburbs of this city do not have rent control. What happens to the rental prices in the suburbs and to the quantity of rental units in the overall metropolitan area, in the city, and in the suburbs? For simplicity, assume that people are otherwise indifferent as to whether they live in the city or the suburbs.
5. (a) The standard theory of monopolistically competitive firms maintains that, in the long run, such firms will operate at less than full capacityT. Does this result depend on whether firms produce identical or differentiated products? Explain.
(b) Suppose the government levies a tax of $1 per unit of output. What will happen in the long run to firms' profits? How does entry or exit affect this result? Explain.