Problem Set 5 ECON 625

29 Jul Problem Set 5 ECON 625

1. Questions 1 through 5 refer to the following scenario. Suppose three firms face the same total market demand for their product. This demand is:

Price (P)	Quantity (Q)
$80	20,000
70	25,000
60	30,000
50	35,000

Suppose further that all three firms are selling their product for $60 and each has about one-third of the total market.

What is the amount of total revenue each firm receives, in dollars?

 

1. Now assume that one of the firms, in an attempt to gain market share at the expense of the others, drops its price to $50. The other two quickly follow suit. What is the amount of total revenue each firm now receives, in dollars, rounded to the nearest dollar?

 

1. What impact has the price drop had on the revenue of each firm?

Each firm has less revenue.

Each firm has more revenue.

The price-dropper has more revenue and the others have less.

The price-dropper has less revenue and the others have more.

 

1. If the firms had all raised their prices to $70 instead of lowering price, what would be the amount of total revenue each firm would have received, in dollars, rounded to the nearest dollar?

 

1. Would the firms have been better off raising the price to $70, lowering to $50, or making no change?

Raising to $70

Lowering to $50

Making no change (keeping price at $60)

 

1. Questions 6 through 10 refer to the scenario that follows. A monopolistically competitive firm has the following short-run inverse demand, marginal revenue, and cost schedules for a particular product:

P = $45 – $0.2Q

MR = $45 – $0.4Q

TC = $500 + $5Q

MC = $5

 

What quantity would maximize profits for this firm? (Hint: Recall that profit maximizing is where MR = MC)

 

1. At what price should this firm sell its product?
2. What would be the amount of the firm’s total revenue at the quantity and price identified in the prior two questions?
3. What would be the amount of the firm’s profit (positive number) or loss (negative number) at the quantity and price identified in questions 6 and 7?
4. What do you think would happen in this market in the long run?

New firms would enter.

Some existing firms would leave.

Some existing firms would stay but no new firms would enter.

There is not enough information to make this determination.

1. Questions 11 through 13 refer to the scenario that follows. An amusement park, whose customer set is made up of two markets, adult and children, has developed demand schedules as follows:

Price ($)	Quantity, Adults	Quantity, Children
5	15	20
6	14	18
7	13	16
8	12	14
9	11	12
10	10	10
11	9	8
12	8	6
13	7	4
14	6	2

 

The marginal operating cost of each unit of quantity is $5. (Hint: Because marginal cost is a constant, so is average variable cost. Ignore fixed cost.) The owners of the amusement park want to maximize profits.

 

Calculate the price, quantity, and profit for each segment if the amusement park charges a different price in each market. (Hint: calculate profit at each price in the adult market, then in the child market, and choose profit maximizing in each. Using a spreadsheet would make this task manageable.)

Adult market price (in dollars): [a]

Adult market quantity: [b]

Adult market profit (in dollars): [c]

Child market price (in dollars): [d]

Child market quantity: [e]

Child market profit (in dollars): [f]

Total profit (adult + child, in dollars): [g]

 

1. Calculate the price, quantity, and profit if the amusement park charges the same price in the two markets combined. (Hint: Add adult and child quantities together, and treat this total and the entire market quantity at each price.)

 

Market price (in dollars): [a]

Quantity (child + adult at this price): [b]

Profit: [c]

 

1. Is profit higher, lower, or the same when the market is split with different prices for adults and for children?

Higher profit with split pricing

Lower profit with split pricing

Same profit with split pricing

Cannot determine with the information available

 

1. Questions 14 through 18 refer to the information that follows. Consider a small town that is served by two grocery stores, White and Gray. Each store must decide whether it will remain open on Sunday or whether it will close on that day. Monthly payoffs for each strategy pair are as shown in the table below.

 

Which firm is the most profitable in this market?

Gray (Profit is highest in every situation.)

White

Neither – they are equally profitable

Neither – there is no profit made by either firm

 

1. What is White’s dominant strategy?

Open Sundays

Closed Sundays

There is no dominant strategy

 

1. What is Gray’s dominant strategy?

Open Sundays

Closed Sundays

There is no dominant strategy

 

1. What will be the likely equilibrium outcome, assuming no additional information is available to either firm?

Both open Sundays

Both closed Sundays

**White open Sundays, Gray closed Sundays

White closed Sundays, Gray closed Sundays

 

1. Is the position identified in question 17 the best possible outcome for both firms?

 

Yes, the position identified in the previous question is the best outcome for both.

No, it would be mutually advantageous to cooperate and choose a different outcome.

Gray could do better, but White is already in the best position and would therefore need an incentive to cooperate.

White could do better, but Gray is already in the best position and would therefore need an incentive to cooperate