Determine firm b profit maximizing output and price
Microeconomics
1. Draw a graph for a CDP firm which faces a demand curve showing Q=0 at P=$12, and Q=8 at P=$8, a SRMC curve which intersects MR at Q=8, and SRATC=$6 at Q=8. What level of output should this firm produce? At that output would the firm make a profit, or loss? How much per unit and in total?
2. Using the same information from the previous question, assume the SRATC changes so that at Q=8 the firm incurs a loss of $2/unit but P>AVC by $2. Redraw the graph and determine the firm’s profit or loss. Will the firm produce in the SR?
3. Suppose you decide to open a gym/health club in Salem. You decide to charge your customers $100/year in membership fees plus a yearly fee. Suppose you know that there are two types of people who will join your club, the Type I people and the Type II people. Type I people had demand: P=200-Q and Type II people have demand: P=400-Q. At a price of $100 how many memberships will you sell to each group (assume Q is determine by the point at which price intersects the demand curves). What is the highest yearly fee you can charge without losing the Type I people?
4. A firm that believes that its customers are either Type A customers or Type B customers. The firm estimates the demand for Type A’s as: P=200-2Q and for Type B’s: P=100- 1/2(Q). Using the point-slope formula for price elasticity of demand, determine which Type has more elastic demand and which has less elastic demand.
5. The demand for a cable television package by Group A is: P=200-Q. For Group B is: P = 500-5Q. Assuming the cable provider can distinguish between the two groups, what is the equilibrium price and quantity for each group assuming that MC=50? What is the amount of consumer surplus for each group?
6. What three conditions are necessary to engage in price discrimination? What are the three kinds of price discrimination that you might find on in a college campus or a college town like WOU’s or Monmouth (provide examples of each)?
7. Allstate Insurance and Aetna are fierce rivals in the insurance industry. The output of insurance policies issued by Allstate is an important factor in Aetna’s decision of how many policies to issue (the number of policies that maximize profits). Similarly, the output of insurance policies issued by Aetna is an important factor in Allstate’s decision of how many policies to issue (the number of policies that maximize profits). The reaction function for Allstate can be expressed as: Qallstate = 100 – 0.5(Qaetna). The reaction function for Aetna is: Qaetna = 50 – 0.25(Qallstate).
a) Graph both reaction functions. Be sure you indicate numerically the points at which each function intersects the horizontal and vertical axes.
b) At which output quantities do the reaction functions intersect?
8. A homogeneous products duopoly faces a market demand curve function of P=300-3(Q), where Q = q1 + q2. Both firms have constant MC = 100.
a. Derive each firm’s reaction function and graph those functions.
b. What is the Cournot equilibrium quantity per firm and the price?
c. What would the equilibrium price and output be if this market were perfectly competitive?
d. What would the equilibrium price and output be if this market were a monopoly?
9. There are two firms in the insurance industry, Firm A and Firm B. Assume each firms acts independently to determine its profit maximizing output of insurance policies and the price of those policies. The demand for Firm A’s policies is P=100-Q and its marginal cost is MC=Q. The demand for Firm B’s policies is P=60-Q and its marginal cost is MC=2Q.
A. Determine each firm’s marginal revenue.
B. Determine Firm A’s profit maximizing output and price.
C. Determine Firm B’s profit maximizing output and price.
Suppose the two firms form a cartel and their joint demand function is P=80-(Q/2).
D. Determine their joint marginal revenue.
E. Determine their joint marginal cost.
F. Determine their profit maximizing output and price.
G. Determine each firm’s quota.
10. Assume the labor market for accountants is competitive. The inverse demand function is P=500-Q and the inverse supply function is: P=140+Q.
A. Solve for the equilibrium wage and quantity of accountants hired. Calculate the consumer surplus, producer surplus and gains to trade. Show on a graph.
B. Now assume that accountants form a labor union and restrict the number of accountants available to work to 120. Assume the demand schedule is unchanged. Calculate the wage, consumer surplus, producer surplus, gains to trade, and deadweight loss. Illustrate with a graph.
C. Suppose there was no labor union for accountants but there was only one firm hiring accountants. Determine the mathematical expression for the marginal cost of labor schedule. How many accountants will be hired and what wage will they receive? At the quantity hired by the monopolist, how much would the monopolist be willing to pay? Calculate consumer surplus, producer surplus, gains to trade, and deadweight loss. Use a graph.
D. Assume the labor market for accountants is a bilateral monopoly, using the equations above, draw a graph of the labor market. How many accountants are hired? What is the highest wage possible? What is the lowest wage possible? What is the deadweight loss?
