Rooster4U and Clucks are huge fast food chains that sell chicken lunch specials. Although both lunches include 2 pieces of chicken, Chicken4U includes waffle fries and a lemonade with its chicken special, while Clucks includes mashed potatoes (with gravy) and a soda. To keep this problem simple, assume that MC = 0.
The national demand for lunch specials at Rooster4U is:
QR = 5000 - 1000Pr + 300Pc
and the national demand for lunch specials at Clucks is:
QC = 3000 - 1500Pc + 225Pr
a. find out the Bertrand best response function for Rooster4U - this should be an expression for PR in terms of PC (Hint: solve first for the profit-maximizing QR in terms of PC and then substitute that expression in for QR in the demand curve to get an equation with only PR and PC - then solve for PR.)
b. find out the Bertrand best response function for Clucks (an expression for PC in terms of PR).
c. What price with Rooster4U charge and what price will Clucks charge?
d. How many meals will each restaurant sell?
e. Based on the information conveyed by the demand curve expressions, how would you describe the price difference between the two meals?