# How much profit would Golden Inn and Village Diner earn if they charged prices of \$165 and \$180 respectively?

The two largest diner chains in Kansas compete for weekday breakfast customers. The two chains Gold Show more The two largest diner chains in Kansas compete for weekday breakfast customers. The two chains Golden Inn and Village Diner each offer weekday breakfast customers a breakfast club membership that entitles customers to a breakfast buffet between 6:00 A.M. and 8:30 A.M. Club memberships are sold as passes good for 20 weekday breakfast visits. Golden Inn offers a modest but tasty buffet while Village Diner provides a wider variety of breakfast items. The demand functions for breakfast club memberships are QG = 5000 25PG + 10PV QV = 4200 24PV + 15PG where QG and QV are the number of club memberships sold monthly and PG and PV are the prices of club memberships both respectively at Golden Inn and Village Diner chains. Both diners experience long-run constant costs of production which are LACG = LMCG = \$50 per membership LACV = LMCV = \$75 per membership The best-response curves for Golden Inn and Village Diner are respectively PG = BRG(PV) = 125 + 0.2PV PV = BRV(PG) = 125 + 0.3125PG A. If Village Diner charges \$200 for its breakfast club membership find the demand inverse demand and marginal revenue functions for Golden Inn. What is the profit-maximizing price for Golden Inn given Village Diner charges a price of \$200? Verify mathematically that this price can be obtained from the appropriate best-response curve given above. B. Find the Nash equilibrium prices for the two diners. How many breakfast club memberships will each diner sell in Nash equilibrium? How much profit will each diner make? (Hint: Use the best response curves to find Nash Equilibrium.) C. How much profit would Golden Inn and Village Diner earn if they charged prices of \$165 and \$180 respectively? Compare these profits to the profits in Nash equilibrium Why would you not expect the managers of Golden Inn and Village Diner to choose prices of \$165 and \$180 respectively? Show less

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