(Price Competition with Capacity Constraint) Two opticians compete on price in the town. The marginal cost for a pair of glasses c = $10 and demand in the town is Q = 100 P per day in April. Assume first that both have a capacity to complete 100 pairs per day, maximum. Also assume both firms are choosing price simultaneously.

1) What is the Nash Equilibrium in prices for these two firms? What is profit for the two firms?

2) Show that there is no profitable deviation from the equilibrium you found above. Now assume that Optician 1 is a bigger outfit and can complete 100 pairs a day maximum, while Optician 2 has fewer employers and can complete 40 pairs per day maximum.

3) Is the Nash equilibrium you found in Part 1 still a Nash Equilibrium? If not, show a profitable deviation. If so, show there is no profitable deviation.

Now suppose there is a shortage of frames because of the shocks on global supply chain. This has caused Optician 1 to only be able to complete 30 pairs per day maximum and Optician 2 to only be able to complete 20 pairs per day maximum.

4) Is the Nash equilibrium you found in Part 1 still a Nash Equilibrium? If not, show a profitable deviation. If so, show there is no profitable deviation.

5) Find a Nash equilibrium in prices and show that there is no profitable deviation. What is profit for the two firms?