Question

Suppose now that market demand for skiing increases to Qᴅ = 9000 − 60p because of environmental regulations neither Pepall Ridge nor Snow Richards can increase their capacities and serve more skiers beyond their current level of 1,800.
What is the Nash equilibrium price outcome for this case? The constant marginal cost is 10.

Answer 1

Price	AR	TR	MR	Profit
80	4200	336000	-	-
90	3600	324000	20	72000
100	3000	300000	40	120000
110	2400	264000	60	144000
120	1800	216000	80	144000
130	1200	156000	100	120000
140	600	84000	120	72000
150	0	0	-	-

As mentioned in the question, both the firms have a supply constraint of 1800 units leading to a total market supply of 3600 units. However each firm can only produce a total of 1800 units. Now in this game matrix , if snow Richards have the choice to choose the pricing strategy first ,it will choose a pricing strategy between 150 to 120 dollars . If he chooses 140 dollar Pepall Ridge would benefit in choosing a price less than snow Richards . This win induce snow Richards to further reduce its price as higher price would lead to shift of market demand to its competitor as he will choose to price his products lower than that of Snow Richards.

If we look at the above game matrix both player come at equilibrium when they both choose the same pricing strategy. If we look at the above table the highest profit earned by the firms would be when they sell 1800 units . Thus in the above game matrix the most efficient outcome would be when both the players chooses to price their products at 90 leading to a consolidated market demand of 3600 and their supply would be 1800 units each which is the highest profit that could be fetched by the firms .