Questions and Answers of Managerial Economics 15th

the effectiveness of advertising by dentists
profitability in the dentist industry When making your recommendation, what account would you take of:
quality of dentist’s services
price of dentist’s services
Would you want to allow advertising by dentists, or would you rather ban advertising by dentists? What effect would your recommendation have on:
Suppose you were a government official in charge of regulating advertising by dentists.
3 In many countries, associations of professionals (dentists, for example)argue that advertising should not be allowed in their industry because it increases competition, creating incentives for
(d) Use your answers to parts 2b and 2c to verify the optimal share of advertising expenditures out of total revenue according to the monopolist’s rule of thumb: εa/εp = a/(p · q).
(c) Use the demand function to solve for the elasticity of demand with respect to the market price εp and with respect to advertising expenditures εa.
(b) Solve for the two first-order maximization conditions, and use them to solve for the monopolist’s optimal market price p* and level of advertising expenditures a*.
(a) Write out the monopolist’s profit function, as a function of the market price p and advertising expenditures a.
2 A monopolist produces a single output q with constant marginal cost c and zero fixed costs. He faces the following demand function:where p is the market price per unit of output and a is
1 In the example in Figure 8.2, what would the payoff matrix look like if advertising by both firms increased each firms revenues by $6 instead of$4? Does this change the Nash equilibrium? Can you
(b) Suppose instead that Nash equilibrium prices were given by:where 1 − a − b < 1. Would an increase in a result in an increase or softening of price competition? Would firm 2’s response be
(a) Will firm 2 respond by increasing or decreasing its price? Does the change in firm 1’s location result in increased or softened price competition?
(c) What happens to market share and profits for each firm as a result of the increase in costs at firm 1?4 Firm 1 and firm 2 sell a similar but differentiated product, charging market price p1 and
(b) What happens to each firm’s price as a result of the increase in costs at firm 1?
(a) What happens to firm 1’s reaction function? What happens to firm 2’s reaction function?
3 Using the information in the previous question, suppose that workers at firm 1 go on strike and demand a higher wage. To settle the dispute, managers at firm 1 increase wages paid to workers, so
(e) Do firms earn positive profits in equilibrium? Does this result confirm or contradict the Bertrand paradox? Explain your answer.
(d) Use the equations of each firm’s reaction function from part (b) to solve for each firm’s equilibrium price pi, level of output qi, and profits .
(c) On a graph with p1 on the horizontal axis and p2 on the vertical axis, graph each firm’ reaction function.
(b) Solve for each firm’s first-order condition, and use it to solve for each firm’s reaction function.
(a) Write out each firm’s profit function, of the form
2 Suppose two firms sell products in a particular market, but consumers do not regard the output of each firm as perfectly identical. The two firms face the following demand curves:Each firm has the
1 Can you use the model of product differentiation to explain the fact that all major brewers introduced a type of ice beer within a very short period of each other? Is this an example of maximal or
5 Refer to Figure 6.3. What would happen if firm 2’s reaction function were steeper than firm 1’s reaction function? Can you relate your answer to stability of the Cournot equilibrium?
4 Suppose that the market demand function is given by:as in Section 6.1.1. Each firm has zero fixed costs and constant marginal cost of productionc. An increase in demand causes the demand function
Using the same demand and cost functions, suppose that firms competed in prices instead of quantities. Solve for the Bertrand equilibrium, including market demand, market price, and profits earned by
2 Suppose instead that firm 1 was the Stackelberg leader in this market. Rewrite firm 1’s profit function, using firm 2’s reaction function, and solve for the Stackelberg equilibrium. Once
(d) Use the demand function to solve for the equilibrium market price, and then solve for the level of profits earned by each firm in equilibrium.
(c) Solve for the Cournot equilibrium
(b) Use the two first-order conditions to solve for each firm’s reaction function, and plot these two reaction functions.
(a) Write out each firm’s profit function, and solve for the two first-order profit-maximization conditions.
1 Consider a market where two firms are competing in quantities. Suppose that the market inverse demand function is given by:Each firm has zero fixed costs and constant marginal cost of production c.
(b) Is firm 2’s best response to ? Why or why not? If not, would firm 2 rather increase or decrease ?5 Repeat Question 4 when actions are strategic complements.6 Consider the reaction functions as
(a) Suppose firm 2 adopts a strategy . Identify firm 1’s best response to and label it .
4 Use a diagram with reaction functions as in Figure 5.8 when actions are strategic substitutes. Notice that when firm 1’s strategy s1 is on the horizontal axis, its reaction function R1 is steeper
(c) Is there a Nash equilibrium (in pure strategies) in this game? Is this game similar to any of the examples of Section 5.4?
(b) Find each player’s best-response strategy, given the strategy played by his/her opponent. Does either player have a dominant strategy?
(a) Write out a payoff matrix which summarizes the strategies and payoffs for each player in this game.
3 Consider the following game describing the agency problem between a supervisor and a laborer. Each player has two strategies. The laborer can either work or shirk, and the supervisor can either
(d) Is this game similar to any of the examples of Section 5.4?
(c) Does either firm have a dominant strategy?
(b) Set up a payoff table like those in Section 5.4, and use it to solve for the Nash equilibrium.
(a) Describe the four elements of this game.
2 Suppose there are two firms, called A and B, which compete with each other in the market for a unique product. Each firm can charge one of two prices for this product: a high price or a low price .
(b) Would this be most appropriately characterized as a non-cooperative game or a cooperative game?
(a) Imagine characterizing the relationship between OPEC members as a game. Identify the four elements of this game. You can find information to answer this question at http://www.opec.org/.
1 Representatives from the eleven member countries of the Organization of Petroleum Exporting Countries (OPEC) meet regularly to set production limits on the number of barrels of oil per day which
(d) Calculate the total revenue, total cost, and the total profit of the monopoly.
(c) Suppose that the monopoly is able to observe who is the rich and who is the poor consumer. Determine the optimal purchase fee charged to the rich consumer (AR) and the optimal purchase fee
(b) Determine the optimal price charged by the monopoly.
(a) With T on the vertical axis and q on the horizontal axis, graph the indifference curves through the origin for the rich and poor consumers. [Hint: for the rich consumer, graph the curve which
6 Suppose there is a monopoly firm using a two-part tariff scheme such that, for q units purchased by a consumer T = A + pq is the total amount the consumer pays to consume the good, made up of a
(d) Determine the firm’s total profits in this case.
(c) Now suppose that price discrimination between the two markets is prohibited. Assuming that the firm charges the same price in each market, determine the profit-maximizing amounts sold in each
(b) Determine the price charged by the monopoly in each market and calculate the total profits of the firm.
(a) Assuming that price discrimination between the two markets is possible, determine the profit-maximizing amounts sold in each market and, hence, the firm’s total output.
5 The cost function for a monopoly is given by C = Q2 + 10Q. The firm sells its output in two distinct markets with (inverse) demand functions given by:
(d) What is the intuition behind this result?
(c) Show that the higher price is charged in the market with the lower elasticity of demand.
(b) Determine the price charged by the monopoly in each market and calculate the total profits of the firm.
(a) Determine the profit-maximizing amounts sold in each market and, hence, the firm’s total output.
4 The cost function for a monopoly is given by C = 100 + 8Q. The firm sells its output in two distinct markets between which price discrimination is possible. The (inverse) demand curves in the two
(d) Calculate the total profit for the firm.
(c) Determine the price charged by the monopoly in each market.
(b) Determine the profit-maximizing amounts sold in each market and, hence, the firm’s total output.
(a) Under what conditions can the monopolist successfully practice price discrimination in these two markets?
3 The cost function for a monopoly is given by C = 5Q. The firm sells its output in two distinct markets with (inverse) demand functions given by:
(d) Calculate the dentist’s profits.
(c) Find the fixed fee the dentist will charge the rich consumer and determine how many visits the individual will make to the dentist.
(b) Find the fixed fee the dentist will charge the poor consumer and determine how many visits the individual will make to the dentist.
(a) Determine the per unit price the dentist will charge.
Assume that the dentist’s total cost function is given by TC = 2q, where q is the number of visits she receives. The dentist is well aware of the possibility of using a two-part tariff scheme to
2 Suppose there are only two consumers in a remote community and one dentist. The demand for dental services from the “poor” consumer is given by:and the demand for dental services from the
(d) Calculate the firm’s total revenue, total cost, and profit.(e) Is it possible for the firm to get any more revenue from this market?Explain.
(c) Determine the total consumers’ surplus and, hence, the fixed fee each consumer pays the firm for the right to purchase the good.
(b) Determine the per unit price that the firm will charge.
(a) Determine the equation of the market demand curve.
1 Suppose there are 100 consumers in a small town, each with an identical demand curve, given by:where q is the amount an individual buys and p is the price they pay.Suppose that a monopoly firm
(f) Does this represent a long-run equilibrium in the industry? Explain.
(e) Determine the output and profits of each firm.
(d) Determine the equilibrium price and quantity in the industry.
(c) Determine the equation for the industry supply curve.
(b) Determine the equation for each firm’s supply curve.
(a) Determine each firm’s marginal cost curve.
8 Suppose a perfectly competitive industry is made up of 100 firms. Suppose each firm has a cost function given by c = q2. Suppose also that the inverse demand curve for the industry is given by p =
(d) Will other firms be attracted to the industry? Explain.
(c) In the long run, will this firm choose to stay in the industry? Explain.
(b) Determine the price the firm will charge, and the profit level at the firm.
(a) Determine the profit maximizing output level for the monopoly.
7 Suppose an industry has only one firm with a cost function given by c =100 + 9q2. The inverse demand curve for the industry is given by p = 20 −q.
(d) Calculate the firm’s cost, revenue, and profit at the profit maximizing output level.
(c) Determine the price the firm will choose to set.
(b) Determine the firm’s profit maximizing output level.
(a) Determine the firm’s revenue function.
6 Suppose a firm facing inverse demand curve p = 10 − 2q has a cost function given by c = 2q2.
(d) Calculate the firm’s cost, revenue, and profit at the profit maximizing output level.
(c) Determine the price the firm will choose to set.

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