ECON 2350 Lecture Notes - Lecture 9: Best Response, Marginal Revenue, Marginal Cost

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amaranthhamster412

27 Feb 2017

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The follower wants to choose an output level such that marginal revenue equals marginal cost: Mr2 = p(y1 + y2) + p y2 y2 = mc2. When the follower increases its output, it increases its revenue by selling more output at the market price. But it also pushes the price down by p, and this lowers its profits on all the units that were previously sold at the higher price. The important thing to observe is that the profit-maximizing choice of the follower will depend on the choice made by the leader. We write this relationship as y2 = f2(y1). The function f2(y1) tells us the profit-maximizing output of the follower as a function of the leader"s choice. This function is called the reaction function since it tells us how the follower will react to the leader"s choice of output. Let"s derive a reaction curve in the simple case of linear demand.

Related Questions

I just need part 3 for this problem!! Thank you!!

Part 1 Suppose the inverse market demand function for a two-firm Cournot model is given by P=49-Q where Q=q_1+q_2 is the total output produced in the market, P is the market price, q_1 is the quantity of output produced by firm 1, q_2 is the quantity of output produced by firm 2. The marginal costs of the two firms are MC1=2 and MC2=3. For a linear inverse demand function P=a+bq, the marginal revenue is given by MR=a+2bq.

1. Find the marginal revenue MR1 of firm 1 as a function of q_1 and q_2.

2. Setting MR1=MC1, determine the reaction function of firm 1.

3. Find the marginal revenue MR2 of firm 2 as a function of q_1 and q_2.

4. Setting MR2=MC2, determine the reaction function of firm 2.

5. What quantity of output will each firm produce? That is, use the two reactions functions to find q_1 and q_2.

6. What is the market price P.

7. Determine the profits of each firm assuming there are no fixed costs.

Part 2 Now, suppose the inverse market demand function for a two-firm Stackelberg model is given by P=49-Q where Q=q_1+q_2 is the total output produced in the market, P is the market price, q_1 is the quantity of output produced by firm 1, q_2 is the quantity of output produced by firm 2. Firm is leader and firm 2 is follower. The marginal costs of the two firms are MC1=2 and MC2=3.

1. What is the follower’s reaction function?

2. Determine the equilibrium output level for both the leader and the follower.

3. Determine the equilibrium market price.

4. Determine the profits of the leader and the follower assuming there are no fixed costs.

Part 3 Use information from parts 1 & 2 to compare the output levels and profits in settings characterized by Cournot and Stackelberg.

upstairsatom

If a monopolist or a perfectly competitive firm is producing at a break-even point, then:
i. average revenue is equal to average variable cost
ii. average revenue is equal to average total cost
iii. total revenue is equal to total variable cost
iv. total revenue is equal to total cost

iii

i and iii

ii and iv

A natural monopoly, such as a local electricity provider, is the result of:
i. a firm owning or controlling a key input used in the production process
ii. economies of scale existing over a wide range of output
iii. long-run average total costs declining continuously as output increases
iv. long-run total costs declining continuously as output increases

What do economies of scale, the exclusive ownership of essential raw materials used in the production process, and patents have in common?

they are all barriers to entry

they all help explain why a monopolists demand and marginal revenue curves are identical

they must all be present before a monopolist may practice price discrimination

they all help explain why a firms short run average total cost curve is U-shaped

#10

The principle that a firm should produce up to the point where the marginal revenue (MR) from the sale of an extra unit of output is equal to the marginal cost (MC) of producing the extra unit applies:

to both perfectly competitive firms and monopolies

only to monopolies

only to perfectly competitive firms

only to firms that can employ discriminatory pricing strategies

#11

A monopoly is producing a level of output such that marginal revenue is equal to marginal cost. The firm is selling its output at a price of $8 per unit and is incurring average variable costs of $5 per unit and average total costs of $10 per unit. Given this information, it may be concluded that the firm:

is operating at maximum total profit

is operating at a loss that could be reduced by shutting down

is operating at a profit that could be increased by producing more output

is operating at a loss that is less than the loss incurred by shutting down

#12

Suppose the demand function for a profit maximizing monopolists good is P = 120 - 0.2Q, its total cost function is TC = 40 + 4Q + Q2, and its marginal cost function is MC = 4 + 2Q. If the firm uses a uniform pricing strategy, then rounded to the nearest unit of output and to the nearest dollar the firm will:

produce 48 units of output, charge a price of $110, and earn a total profit of $5280

produce 48 units of output, charge a price of $110, and earn a total profit of $2744

produce 52 units of output, charge a price of $134, and earn a total profit of $5322

produce 52 units of output, charge a price of $134, and earn a total profit of $4016

magentabuffalo597

Robert's New Way Vacuum Cleaner Company is a newly started small business that produces vacuum cleaners and belongs to a monopolistically competitive market. Its demand curve for the product is expressed as Q = 5000 - 25P where Q is the number of vacuum cleaners per year and P is in dollars. Cost estimation processes have determined that the firm's cost function is represented by TC = 1500 + 20Q + 0.02Q².

Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary.

a. What are the profit-maximizing price and output levels? Explain them and calculate algebraically for equilibrium P (price) and Q (output). Then, plot the MC (marginal cost), D (demand), and MR (marginal revenue) curves graphically and illustrate the equilibrium point.

b. How much economic profit do you expect that Robert's company will make in the first year?

c. Do you expect this economic profit level to continue in subsequent years? Why or why not?

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ECON 2350 Lecture Notes - Lecture 9: Best Response, Marginal Revenue, Marginal Cost

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