ECON 2300 Lecture Notes - Lecture 11: Best Response, By2

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amaranthhamster412

6 Feb 2017

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In a cournot equilibrium, each firm is maximizing its profits, given its beliefs about the other firm"s output choice, and, furthermore, those beliefs are confirmed in equilibrium: Each firm optimally chooses to produce the amount of output that the other firm expects it to produce. In a cournot equilibrium neither firm will find it profitable to change its output once it - discovers the choice actually made by the other firm. The cournot equilibrium is simply the pair of outputs at which the two reaction curves cross. At such a point, each firm is producing a profit-maximizing level of output given the output choice of the other firm. Recall the case of the linear demand function and zero marginal costs that we investigated earlier. We saw that in this case the reaction function for firm 2 took the form y2 = a bye 1 2b .

Related Questions

The market for authentic poutine in Vancouver is controlled by two shops, PierrePoutine (i = P) and MeanPoutine (i = M). The market demand is given by p = 12âq, where p is the price, and q is aggregate output. Both shops produce at constant marginal cost of $ 2 per dish of poutine.

a) Suppose first that each firm i = 1, 2 chooses its output qi , taking the output of the other firm as given [Cournot Competition]. Aggregate output is thus q = qP + qM. Determine the best-response functions q br 1 (q2) and q br 2 (q1). Calculate the Nash equilibrium quantities, the market price, and profits (Note that everything is symmetric here).

b) Now suppose firm i = 1,2 chooses its price pi , taking the price of the other firm as given [Bertrand Competition]. Give the Nash equilibrium prices and quantities. Explain carefully why i) this is a Nash equilibrium and why ii) there is no other equilibrium. Note: most of the credit will be for your explanation.

c) What if Pierre Poutine finds a cheaper cheese curd supplier, which reduces its marginal cost to $1 instead (MeanPoutine continues to have $ 2 production cost). Assuming that prices are quoted in dollars and cents (the smallest unit of measurement is a cent), determine new Nash equilibrium prices and quantities for the Bertrand Competition situation. Explain!

1-7 True or False

1) In the short run, a perfectly competitive firm can earn positive, zero, or negative profit depending on the market price of the firm's output.

2)In the model of the perfectly competitive firm, the firm's fixed costs are equal to its implicit costs of production.

3)Assume the market price is greater than average total cost at the perfectly competitive firm's profit-maximizing level of output. In this case, the firm is earning positive economic profits, which act as an incentive for new firms to enter the market.

4)Assume that at the current level of output, price equals marginal revenue, but is less than average total cost. So long as price is greater than average variable cost, the firm should continue to operate in the short run to minimize its losses.

5)The fact that a firm is a price-setter does not ensure it will make a positive economic profit in the short run and over time.

6)Barriers to entry serve to limit the number of firms that operate in a particular market and, as 11) such, reduce the amount of total profit earned in the market.

7)In the prisoner's dilemma game, each player's dominant strategy is also the Nash equilibrium.

14-17 Multiple Choice

14) Marginal revenue is equal to:
A) the change in P x Q due to a one unit change in output. B) the change in quantity divided by the change in price.

C) the change in price divided by the change in output. D) price, but only if the firm is a price searcher.

15) In order to maximize its profits, a price-taking firm should produce the level of output at which:

A) marginal revenue = marginal cost. B) total revenue = total cost.

C) variable revenue = variable cost. D) average revenue = average cost.

16) Assume that there is an improvement in the technology used by firms in a perfectly competitive industry that is initially in long-run equilibrium. In the short run this would cause:

A) cannot be determined with the information given. B) no change in the firm's economic profit.
C) a decrease in the firm's economic profit. D) an increase in the firm's economic profit.

17) Assume at the firm's profit-maximizing level of output P = AVC. In this case, the firm will be:

A) incurring an economic loss. B) earning a positive economic profit.

C) earning economic profit = 0. D) breaking even.

1. Suppose that a perfectly competitive firm's Total Cost function is given by:
TC = 50 + 80q - 10q² + 0.6q³
a. What is fixed cost equal to? What is Variable Cost equal to?
b. What is Marginal Cost equal to? What is the Average Variable Cost equal to?
c. Find an equation for the inverse supply curve of the firm. Hint: the supply curve presumes profit-maximizing outputs at any market price.
d. Below which market price (a number) will this firm choose to produce 0 output?
e. Choose a market price that is between Average Cost and Average Variable Cost. Will, the firm choose to produce a positive output level?
Depict this output level in a graph that includes all the
appropriate curves. Explain verbally (and with numbers) why this firm would choose to produce the output you chose.
f. What does it mean for a firm to be a price taker? What is the
implication of this for the individual firm's demand curve? You must also mention in your answer the term elasticity (correctly of course).
g. If the firm's cost curve shifted down, what would this do to?
the firm's supply curve? Justify your answer with an example using the short-run total cost curve above.
Q2. Suppose there are two demand curves (e.g two different sets of consumers) for a particular product (two distinct markets that can be segmented-so somehow the consumers in one market cannot buy in the other market and resale from lower-priced consumers to higher-priced consumers is not possible).
The two demand curves are given by the following equations:
Q1 = 14 - P1 (group 1)
Q2 = 12 - 2P2 (group 2)
a. Solve for the inverse demand curve for group 1 and then graph the inverse demand curve with P on the vertical and Q on the horizontal axis.
b. Calculate MR for each group above and graph on the graphs in part a.
c. Suppose MC=AC is constant and equal to 2 for the firm (So the MC curve applies for both groups (because it is the same supplier of a single product for the two groups), although demand and MR are unique to each group since the markets can be segmented. Find the profit-maximizing output, price, and profits in each market. You may assume that TC = AC*Q (cost per unit*number of units). Label the correct price and quantity for each graph in part a.
d. What are the elasticities at the profit-maximizing quantities that you found in part c?
e. Can you say anything about how the price charged in each market relates to the relative price elasticities of demand you calculated in part d? Try to explain intuitively using an example of a real product that you might consume, in which the supplier of a single product can segment the market and in fact charge different prices to two different groups.
f. Now suppose that the above firm cannot segment the two markets. Solve for the single profit-maximizing price and quantity. What are profits equal to?

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ECON 2300 Lecture Notes - Lecture 11: Best Response, By2

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