Question

Authentic Car Services is the only transportation provider in a midsized county, about 65 miles outside of a major city. Licensed by the local government, the firm provides door to door service between the residents’ homes, the train station (which connects to the major city), local retail stores, and other key locations within and surrounding the town center. To access the service, residents may call for a specific pick-up time, or they could wait by any curb for an unscheduled curbside pick-up.

The market demand for transportation services is described by the equations: P = 8 – 0.015Q and MR = 8 – 0.03Q, where Q is the number of trips per week.

With regular maintenance on its fleet of vehicles as well as outstanding loan payments, the firm faces a weekly fixed cost of $200.

Authentic Car Services’ labor force includes drivers and dispatchers, and all report to work if the firm is providing service. Along with the labor force and the necessary materials needed for day-to-day operation, the firm’s additional costs can be described by the equations: MC = 2 + 0.01Q and AVC = 2 + 0.005Q, where Q is the number of trips per week.

1. Currently, Authentic Car Services provides _________ trips per week and charges $_________ for each trip.

2. At the current profit-maximizing quantity, Authentic Car Services’ profit is $______ per week.

3. The current market outcome ______ (either is or is not | is | is not ) efficient and a measure of this ______ (efficiency | efficiency or inefficiency | inefficiency) is $ _______.

Now consider that consumers’ income increases, and transportation services is a normal good. As a result, the new market demand for transportation services is described by one of the following equation sets:

Equation A: P = 7 – 0.015Q, and MR = 7 – 0.03Q

Equation B: P = 10 – 0.015Q and MR = 10 – 0.03Q

The market fully adjusts after the demand shock.

4. As a result of the shock, the new market demand is described by Equation ____ (A | B) .  Authentic Car Services now provides ______ trips per week and charges $_____ for each trip.

5. As a result of the shock, consumers’ surplus has decreased. Now, Authentic Car Services has _________ (a higher | a lower | no change in its) economic profit, and the overall market _______ (efficiency | efficiency or inefficiency | inefficiency) has _________ (decreased to | increased to | remains the same at ) $.___________.

Answer 1

The above question can be solved as follows:

1) Since Authentic Car Servives operates as a monopoly in the market, its equilibrium would occur at a point where the marginal revenue and marginal cost are equal i.e.

MR = MC

8-0.03Q = 2+0.01Q

6 = 0.04Q

Therefore, Q = 6/0.04 = 150 trips/week. At this quantity, Price is equal to

P = 8-0.015*150 = $5.75. Hence, the equilibrium price is $5.75 and equilibrium quantity is 150 trips/week.

2) The Profit at equilibrium/profit maximizing quantity is given by;

Profit = Total Revenue - Total Cost

= P*Q - (Total fixed cost + total Variable cost)

= 5.75*150 - (200 + Q*AVC)

= 862.5 - [200 + (2*Q + 0.005Q^2)]

= 862.5 - [200 + (2*150 + 0.005*150^2)]

= 862.5 - [200 + 300 + 112.5]

= 862.5 - 612.5 = $250

Therefore, profit is equal to $250.

3) A monopolist produces less output and charges a higher price as compared to higher competitions (like Perfect Competion). It charges a higher price than its marginal cost due to which it distorts allocation of resources. The loss in output (when compared with the perfect competition output) involves a total loss in consumer surplus. A part of this loss is transferred to the producers in the form of producer surplus but the rest accounts for the dead weight loss, a cost of market inefficiency.  

Thus, in the above question the market outcome is inefficient and the measure of this inefficiency is the dead weight loss incurred which is given by;

DWL = 0.5 (Price charged by the monopolist -Price Charged under perfect competion) (Output under prefect competion- output under monopoly)...................................................................................................................(a)

Under perfect competition, the equilibrium occurs at

P = MC

8-.015Q = 2+0.01Q

6 = 0.025Q

Therefore, Q = 6/0.025 = 240 trips/week &

P = 8-0.015*240 = 8-3.6 = $4.4

Now, substituting the values in equation (a) , we have

DWL = 0.5 (5.75-4.4) (240-150)

= 0.5 (1.35) (90) = $60.75

4) Since, the transportation services is a normal good with the increase in income of the consumer, the demand curve of these services will shift to the right indicating an increase in demand. The demand curve equations which showcase this increase are;

Equation B: P = 10 – 0.015Q and MR = 10 – 0.03Q.

[Equation A: P = 7 – 0.015Q, and MR = 7 – 0.03Q, this equation set indicates a decrease in demand, which is not possible in the above case of income increase considering the services to be a normal good, hence, it is rejected.]

Calculation of the new equilibrium;

MR = MC

10 – 0.03Q = 2+0.01Q

8 = 0.04Q

Therefore, Q = 8/0.04 = 200 trips/week. At this quantity, Price is equal to

P = 10-0.015*200 = 10-3 = $7.Hence, the new equilibrium price is $7 and the new equilibrium quantity is 200 trips/week.