Question

Do question 3: Sequential quantity choice please

Question 2: Simultaneous quantity choice Two forms F1 F2 produce home product and compete on the same Themat described by the inve c e P-11-20. Whet her output and Pis the market price Top this simple w ow that each firm cam produce either lo units there the coll e c t ion Further power that both firm we ac c etta 2 se that the total cost of fimi-1.2 pedacin i ty (1.2) is by Cla) Further uppe that production chce m e I Since each firm can choose to pos t there for posible combinations of output choices = (1, 1), (2.1). 1.2. 2. the P e ach 2. If the firm chce output why ), then firm w only) O utput at the market pricep determined by total output + Firm I prot is therefore ivy -2. Bearing in mind bow (n.) affect Pervaluate this profit function for c ombination of output ca are the Bearing in mind that the firms are w mirror image of firm 1), represent the ere so that firm s wo matrix of this game Find the Nash equilibria of this game. Question 3: Sequential quantity choice Now cost exactly the same firme in demand function, cont function and quantity choices above. In contrast to before, however, suppone that in Iches its quantity first, the firm 2 observes firm 's quantity choice and chooses its quantity 1. Draw the game tre for this game in the past f ew 2. What is Firm 's strategy we? What is Firm strategy t o brin mind that a strategy is a complete contingent plan for how to play the Using backwand induction predict the outcome of this Disco D w ing first benefit Firm 1

Answer 1

Given the inverse demand curve, P = 11 - 2Q

Each firm can produce either 1 or 2 units.

Both firms have a constant marginal cost equal to 2.

1. The market price under each of the possible output choices can be seen as,

Price Firm 2 1 unit 2 units Firm 1 1 unit 2 units

These are computed by putting the value of total output in the inverse demand curve to get the value of Prices.

2. x1 = Pq1 - 2q1

This is the realised profit for firm 1. Putting the values of P in this equation and q1, for each scenario to get the realised profits for each case as,

Profit Firm 1 Firm 2 1 unit 2 units Firm 1 1 unit 2 units

3. The payoff matrix for this game is given below.

Payoff Firm 2 1 unit 2 units 5,5 3,6 6,3 2,2 Firm 1 1 unit 2 units

4. The Nash equilibria of this game are (6, 3) and (3, 6).

This is computed by checking the best response strategy for each firm 1 given that the other firm chooses a given strategy, then the strategies that are selected by both the firms are the Nash equilibria.

For example, if firm 2 chooses to produce 1 unit, then firm 1 would choose to produce 2 units, then if firm 2 chooses to produce 2 units, then firm 1 would choose to produce 1 unit.

Then similarly, it can be seen for firm 2 given that firm 1 chooses a strategy, then the strategies that are chosen by both the firms are Nash equilibria, which are (6, 3) and (3, 6).

Question 3:

Given the sequential game, where firm 1 chooses its output initially followed by frim 2 choosing the output.

1. The game tree for this game is given as,

(22 (55 (22)

2. Firm 1's strategy set includes choosing either 1 unit or 2 units to produce.

Firm 2's strategy set includes 4 strategies, choosing 1 unit given that firm 1 chose 1 unit to produce, choosing 2 units given that firm 1 produces 1 unit, choosing 1 unit given that firm 1 chooses 2 units to produce and choosing 2 units given that firm 1 produces 2 units.

3. Using backward induction, the output of this game would be (6, 3).

First, firm 2 chooses what to produce in both the scenario, that is given that firm 1 chooses to produce 1 unit or 2 units. Then firm 1 chooses which of the strategy is better among the ones chosen by firm 2. This will be (6, 3).

Yes, moving first benefits firm 1 as it makes a profit of 6 while firm 2 makes a profit of 3. If firm 2 would move first, then firm 2 would make a profit of 6 while firm 1 will make a profit of 3. From this, it can be stated that moving first does benefit firm 1.