L Jeans and M Jeans are duopolists that produce jeans in a differentiated goods market. The market demand for L Jeans is yL = 80 – pL + 12pM , whereas the market demand for M Jeans is yM = 160 – pM + 12pL . L Jeans’ cost function is CL(yL) = 80yL , whereas M Jeans’ cost function is CM (yM) = 160yM.
a)
Calculate the Bertrand equilibrium in this market. Indicate each firm’s price, output level, and profits.
b)
Find prices and output levels that would maximize joint profits, and calculate the maximum joint profits