Dr. Barry Haworth
University of Louisville
Department of Economics
Economics 301
Summer 2000

Exam #2

(Questions and Suggested Answers)

Section 1: Answer parts a-e of question #1 below
1. Gas stations operate in a perfectly competitive industry. The costs facing each station are given by (note: q = gallons of gasoline sold in one day)

Total Variable Costs = 0.001q2 - q
Sunk Costs = 5000
Recoverable Fixed Costs = 4000
Marginal Cost = 0.002q - 1

a. Describe how prices and output are determined in the perfectly competitive industry/firm model.

To best understand how prices and output are determined in perfectly competitive markets, we must remember that firms are price takers in this setting. That is, the market price is set collectively by demanders and suppliers. Below, for example, an equilibrium price like $22 would be determined by the market graph on the right side where Demand = Supply.

Once determined, firms react to this market price by deciding how much output to produce. In the left side graph, firms take the price as "given" and then choose output where that market price equals their marginal cost. Firms in this example choose output levels of 10 units.

b. If the gas prices are $2, then what are the highest profits earned by each gas station?

The first step here is to determine how much the firm should produce. Firms produce where P = MC, so we set the MC equation equal to the price of $2 and solve for q.

P = MC
2 = 0.002q - 1
q* = 1500

The second step is to calculate profits (p). To do so, we must use the information above to obtain total cost. Total cost is the sum of Variable and Total Fixed Costs, while Total Fixed Costs are the sum of all Sunk Costs and all Recoverable Fixed Costs.

TC = VC + Sunk Costs + Recoverable Fixed Costs
TC = (0.001q2 - q) + 5000 + 4000
TC = 0.001q2 - q + 9000

We "plug in" q = 1500 to this equation, and calculate profits as the difference between Total Revenue and Total Cost.

p = Pq - TC
p = (2)(1500) - (0.001(1500)2 - (1500) + 9000)
p = 3000 - 9750 = -6750

This firm makes a loss of $6750 when producing 1500 units. However, by shutting down (i.e. producing zero units of output), the firm only pays its sunk costs of 5000. Therefore, the highest profits the firm can earn is p = -5000.

c. Given your results in part b, this industry will change in the long run. Compare the changes that would occur if there are increasing returns to scale within the industry to those that would occur if there were decreasing returns to scale within the industry.

If firms are making losses in the short run, then this creates an incentive for firms to exit. In the long run, this (exit) will occur. The graph below illustrates this basic result.

Intersection between the short run Supply curve (S1) and Demand curve occurs below the long run Supply curve (LRS). This gives a price of P* that leads to losses. As firms exit the market, the short run Supply curve shifts left (to S2 and then to S3, and finally to S4). When the Supply curve stops at S4, the process stops and the price becomes P**.

The end result of this exit differs slightly, however, when we compare the situation involving increasing and decreasing returns to scale. If there are decreasing returns to scale, then there are increasing costs and the LRS curve has a positive slope. As the short run Supply curve decreases (along LRS), prices slowly rise, but not by as much as when the LRS curve has a negative slope (as is the case with increasing returns or decreasing costs).

d. How do the characteristics of this industry lead to each firm charging the same long run market price and making zero profits?

Firms charge the same long run market price because they sell homogeneous goods and because the price is given to them by the market. In the answer to part a, the process of how price is determined by the market is described. When one firm's product is a perfect substitute for another firm's product, of course, there is no reason each firm's price should differ anyway, and so all firms charge the same price. Firms make zero profits in the long run because there are no barriers to entry. When firms make greater than zero profits, then other firms have an incentive to enter the market. As they do so, the short run supply curve increases, and continues to do so until all firms are making zero economic profit. Similarly, when firms make negative economic profits, there is an incentive to exit. Firms exit until zero economic profits are reached. Therefore, over the long run, profits remain at zero.

Assume that crude oil is supplied within a perfectly competitive market.
e. Briefly discuss how US suppliers and consumers (refineries) in the crude oil market are affected by our country's being open to international trade.

When the country opens to international trade, we see two prices for crude oil. This is illustrated in the graph below.

One price is that charged (initially) by domestic suppliers (PD). The other price is the international price (PW). If the domestic price exceeds the international price, as it does on the graph, then demanders will buy some combination of imports from the foreign suppliers and domestically supplied crude oil. The lower the international price, the more imports there are. On the graph, we see that the difference between domestic (US) supply and overall supply is given as the quantity of imports.

Section 2: Answer any two of the following three questions
1. Assume that a small firm produces with both skilled and unskilled labor. Address the following situations (separately) using isoquant/isocost analysis.

a. Modest increases in the minimum wage are accompanied by tax breaks for small firms which lower the total cost of these firms. The tax breaks are designed to offset the increased cost of hiring unskilled labor.

The first issue to address is how firms use isocost and isoquants. Unlike indifference curve analysis, where the expenditure is given and you choose an indifference curve, isocost/isoquant analysis has firms deciding on their level of output (isoquant) and then choosing the lowest isocost line to produce on.

The minimum wage and tax break both affect each firm's isocost. The isocost equation is given here as (L1 and L2 are skilled and unskilled workers, resp., and w1 and w2 are the wages of skilled and unskilled workers, resp.):

w1L1 + w2L2 = TC

The isocost can be rewritten as: L1 = -(w2/w1)L2 + TC/w1

Minimum wages cause w2 to increase. This causes the slope of the isocost (-(w2/w1)) to increase. If the firm chooses to produce the same level of output (i.e. operate on the same isoquant), then the firm will produce at a point that is further up the isoquant. For example, using the graph below, the isocost might shift from the blue line (and intersection at pt. A) to the red line (and intersection at pt. B).

If the firm gets a tax break, then it is less expensive to produce the current level of output. The firm can decide whether to produce more output at the same cost (a higher isoquant) or the same level of output at lower cost. In the graph above, the firm could move to pt. C and a higher isoquant.

b. The firm decides to provide training for its employees, and the training raises the productivity of both types of worker.

When productivity increases, the firm is able to produce the same output level, but with fewer laborers than before. That allows the firm to select an isocost line where total cost is lower, but that intersects an isoquant associated with output that is no different than before. Put another way, this is equivalent to the isoquant shifting inward. In the graph below, we see this as movement from I1 to I2, where 1000 units are produced with both isoquants.

2. Assume that the market for rental housing is perfectly competitive with the following demand and supply information (math required on this problem, but a solid discussion here makes partial credit a possibility also):

Market Demand: QD = 1400 - 2P
Market Supply (SR): QSRS = 200 + P
Market Supply (LR): QLRS = -200 + 2P

(QD = quantity demanded in the market, QSRS = quantity supplied in the short run, QLRS = quantity supplied in the long run, P = price of rental housing)

a. How would a $200 price ceiling directly affect this market in the short run?

To know how the price ceiling actually affects this market, we must determine whether the ceiling is placed above or below the equilibrium price. We find the equilibrium price by setting QSRS = QD and solving for P.

1400 - 2P = 200 + P
P* = 400

Because P* is higher than the price ceiling of $200, there will be a shortage. To determine how much of a shortage, we plug in 200 for P in the demand and (short run) supply equations and solve for quantity.

QD = 1400 - 2(200) = 1000
QSRS = 200 + (200) = 400

The difference between QD and QSRS is the amount of the shortage. It is 600 units.

b. How would a $200 price ceiling affect consumer and producer surplus in this market (in the short run)?

When a price ceiling constrains the market from achieving equilibrium, the consumer and producer surplus change. We can calculate these changes, but before doing so, it is helpful to consider how the ceiling affects things graphically. The graphs below show the changes in consumer surplus (blue area) and producer surplus (green area).

Prior to the price ceiling, both of these surpluses can be calculated as the area of a triangle (note that we must deduct the yellow triangular area from producer surplus), as shown below. We'll call consumer surplus CS and producer surplus PS.

CS = (700 - 400)(600)(1/2) = 90,000
PS = (400 - (-200))(600)(1/2) - (0 - (-200))(200)(1/2) = 160,000

After the price ceiling, the surpluses are (note that CS is the sum of the area of the upper triangle and the lower rectangle):

CS = (700 - 500)(400)(1/2) + (500 - 200)(400) = 160,000
PS = (200 - (-200))(400)(1/2) - (0 - (-200))(200)(1/2) = 60,000

The price ceiling causes consumer surplus (CS) to increase and producer surplus (PS) to decrease.

c. How would this market react in the long run to the $200 price ceiling?

Note first that, before the price ceiling, the demand curve and short run supply curve intersected at a point on the long run supply curve. This implies that the price ceiling moved this market off its long run supply curve, which should lead to an adjustment period where firms will exit until the market is at a point of equilibrium with each of the three curves. As a result, the shortage will worsen over the long run.

To determine how much worse the shortage will get, we plug in 200 for P in the demand and (long run) supply equations and solve for quantity.

QD = 1400 - 2(200) = 1000
QLRS = -200 + 2(200) = 200

The difference between QD and QLRS, 800 units, is the amount of the shortage after firms exit and the short run supply curve decreases along the long run supply curve. As stated above, the shortage clearly worsens over the long run.

3. Firm A is perfectly competitive with the following (monthly) short run cost curves:

TC = (1/3)q3 - q2 + 10q + 100
MC = q2 - 2q + 10

(math is required on part a, but partial credit is possible for a good discussion)
a. If all of this firm's fixed costs are sunk, then how much output does the firm produce each month at their "shut down point"?

Answering this question requires that we set average variable cost equal to marginal cost (because they intersect at the shut down point), and solve for output. First, we must find average variable cost from TC above. Total variable cost (VC) is that part of TC that varies with changes in output. Therefore, VC = (1/3)q3 - q2 + 10q. Dividing VC by q, we get AVC = (1/3)q2 - q + 10.

(1/3)q2 - q + 10 = q2 - 2q + 10
q((2/3)q - 1) = 0
q = 3/2

The firm produces 3/2 units of output at their shut down point.

b. If this firm is required (by the government) to pay a $100 license fee each month, then discuss how consumer and producer surplus, and the firm's profit maximizing choice of output are affected.

When a $100 fee is added each month, we see that the fee does not depend on how much output is produced. Costs that are independent of output are, by definition, fixed costs. MC is defined as the change in TC with small changes in output. Fixed costs don't change with output, so they don't affect TC when output changes (hence don't affect MC). MC is what firms use to determine output levels, so if there is no change in MC there is no change in output. With no change in output, there is no change in the surpluses (excepting for the fact that the additional $100 per month is taken from producer surplus).

c. Suppose the government decides to charge a $5 fee on every unit of output each month. Discuss how consumer and producer surplus, and the firm's profit maximizing choice of output are affected.

When each unit is $5 more expensive to produce, the MC of producing an additional unit is more. Therefore, an increase in MC causes a change in output. As MC rises, output decreases. The decrease in each firm's MC also causes the market supply curve to decrease. Decreasing market supply leads to a higher market price. The higher price makes consumer surplus smaller, and the decrease in market supply leads to smaller producer surplus as well.