2. There are one supplier S that produces a good at no cost and two retailers R and R that compete in quantities and face the inverse demand P=4-9R9R, where, for each i = 1,2, qr, is the quantity that R, buys from S and sells to consumers. The timing of the game is as follows. First, S chooses its price s. Then, the two retailers observes and simultaneously choose their quantities qR and qR. (a) (15 points) Calculate the equilibrium values for s, qR, and qR. Suppose now that S and R merge to become the integrated firm I. Firm I produces at no cost, sells to R at price s, and sells directly to consumers at price P=4-91-9R Firm R buys from firm I at prices and sells to consumers at price P=4-91-9R The timing of the game is as follows. Firm I first sets the price s at which it sells to R2. Then, having observed s, I and R simultaneously set their quantities qr and e d qR. (b) (10 points) Write down the profit of both firms as functions of s, q1, and qR. (c) (15 points) Calculate the equilibrium values for s, qr, and qR. (d) (10 points) Without doing any additional calculations, determine whether the merger is good or bad for consumers. [max: 50 words] 2. There are one supplier S that produces a good at no cost and two retailers R and R that compete in quantities and face the inverse demand P=4-9R9R, where, for each i = 1,2, qr, is the quantity that R, buys from S and sells to consumers. The timing of the game is as follows. First, S chooses its price s. Then, the two retailers observes and simultaneously choose their quantities qR and qR. (a) (15 points) Calculate the equilibrium values for s, qR, and qR. Suppose now that S and R merge to become the integrated firm I. Firm I produces at no cost, sells to R at price s, and sells directly to consumers at price P=4-91-9R Firm R buys from firm I at prices and sells to consumers at price P=4-91-9R The timing of the game is as follows. Firm I first sets the price s at which it sells to R2. Then, having observed s, I and R simultaneously set their quantities qr and e d qR. (b) (10 points) Write down the profit of both firms as functions of s, q1, and qR. (c) (15 points) Calculate the equilibrium values for s, qr, and qR. (d) (10 points) Without doing any additional calculations, determine whether the merger is good or bad for consumers. [max: 50 words]