Suggested Answers: Midterm #3 Exam preparation exercises

Econ 301 - Haworth

1. A monopolist faces the following demand and marginal revenue curves:

Demand Q = 60 – P

Marginal Revenue MR = 60 – 2Q

The monopolist faces constant average and marginal costs, such that: AC = MC = 10.

a. What output level and price maximize this monopolist’s profits?

b. What are the most profits that this monopolist can earn?

Set MR = MC and solve for Q*

60 – 2Q = 10

Q* = 25

Plug Q* into Demand and solve for P*

(25) = 60 – P

P* = 35

Plug Q*, P* and AC into the profit equation

p = (P* - AC)Q*

p = (35 - 10)25 = 625

Assume that the market changes, so that the “new” demand and MR curves are steeper (i.e. more inelastic). Those new curves are given as:

New Demand Q = 55 – 0.5P

New Marginal Revenue MR = 110 – 4Q

c. What is the new profit maximizing level of output, the new price, and new level of profits?

Similarly, we solve for Q*, P* and profits.

Set MR = MC and solve for Q* Plug Q* into Demand and solve for P*

110 – 4Q = 10 (25) = 55 – 0.5P

Q* = 25 P* = 60

Plug Q*, P* and AC into the profit equation

p = (P* - AC)Q*

p = (60 - 10)25 = 1250

d. Compare the Dead Weight Loss (DWL) of these two settings. Which has greater DWL?

The graph associated with these two curves will look as follows

For the first pair of equations (corresponding with D₁ and MR₁), DWL is the yellow area. For the second set of equations (corresponding with D₂ and MR₂), DWL is the yellow and “rose” areas combined.

First set of equations (DWL₁) = (1/2)(35 – 10)(25) = 312.5

Second set of equations (DWL₂) = (1/2)(60 – 10)(25) = 625

DWL has increased.

2. Firms would be better off in the long run if they could slow down the entry of rival firms. As entry becomes more difficult, firms have greater opportunities to secure greater than zero long run profits.

a. Is it possible for firms to make entry more difficult?

The ease of entry depends upon the barriers facing the potential entrants. Firms can make entry more difficult in several ways. One way is by lowering costs, allowing a firm to maintain a cost advantage over potential entrants. This creates a natural barrier to entry. Another way is though pricing. A firm can set a price that is too low for entrants to profitably compete.

b. What kinds of strategic actions might deter entry?

Firms can act to preempt entry by lowering their costs or though limit pricing. In each case, the incumbant firms make it unprofitable for entrants to come into the market and compete against them.

c. Do incumbant firms (i.e. existing firms) possess advantages over potential entrants when choosing these strategies?

Yes, incumbant firms have first mover advantages. These firms are able to establish a consumer base. The extent to which this advantage is helpful depends upon the “costs” of switching to rival products.

3. Suppose advertising expenditures are able to increase a firm’s sales.

a. Describe a model that helps a firm to decide on the profit-maximizing level of advertising.

Advertising would affect the demand facing a firm. Firms use ads to affect the preferences and tastes of consumers, and then influence buying patterns. Advertising expenditure could enter into our model by being including in demand function. Advertising also represents a cost to the firm. It is quite likely to be a fixed cost, however, as advertising does not likely vary with the output of a good.

b. Describe the marginal rule that a firm should use with advertising expenditures.

Firms should change their advertising expenditures until the marginal benefit of advertising equals the marginal cost of advertising. Benefits would be in terms of sales, while costs would involve the advertising expenditures themselves.

4. Bill and Ted will play a game of “chicken”, where both speed in their car toward one another on a single lane road. The first to veer off is the chicken, whereby the other is considered a hero and reaps the appropriate benefits from his “hero-dom”. If neither veers, then both die a painful, fiery death.

In the matrix below, the payoffs (in terms of utility) for this game are given.

a. What type of game is this?

Simultaneous game. Both players move at the same time.

b. Does this game have a Nash equilibrium?

We can determine whether there is a Nash equilibrium as follows

For Bill:

If Ted veers away, then Bill’s best strategy is don’t veer away.

If Ted doesn’t veer away, then Bill’s best strategy is to veer away.

For Ted:

If Bill veers away, then Ted’s best strategy is don’t veer away.

If Bill doesn’t veer away, then Ted’s best strategy is to veer away.

Clearly, there is more than one Nash equilibrium. The result will either be where Bill veers away and Ted doesn’t, or where Bill doesn’t veer away and Ted does. That is, both will choose a strategy that is different from the other.

c. Is a threat by either Bill or Ted to not veer away (i.e. not be a chicken) a credible threat?

In this case, because both have situations where not veering away is a dominant strategy, the threat is credible. A credible threat involves threatening to utilize a strategy that yields a greater payoff than alternative strategies.

Suppose Bill removed his steering wheel, making it impossible to veer away. Once removed, Ted must determine a strategy as the game begins.

d. How has Bill changed the nature of this game?

Bill has transformed this simultaneous game into a sequential game. Bill has decided upon a strategy of “don’t veer” and now Ted must decide upon his strategy. Both players move in turn, making this a sequential game now.

e. Would Bill’s precommitment to the “don’t veer” strategy make Bill better off?

Yes, Bill’s precommitment to the “don’t veer” strategy makes Bill better off because this move ensures that the pair will reach only one of the two Nash equilibria. One of these equilibria involves Bill receiving 1 unit of payoff (e.g. 1 util of satisfaction), the other involves Bill receiving 3 units. Bill’s precommitment has moved the game into the second column and allowed Bill to receive the 3 unit payoff.