Economic question

4. Collusion (25 points) Consider a market with two rms, 1 and 2, that manufacture a homogenous product. The inverse demand for the product is: P(Q) = 1200 262 where Q is total output. Production costs for each of the two rms is identical and given by C(qi) = 100:},- where q, is rm 's output. Thus, Q = q1 + Q2. (a) (2 points) Write out the prot function of rm 1. (b) (4 points) Assume rms play the static Cournot equilibrium. Compute the best response function for each rm. (c) (4 points) Compute the Nash equilibrium level of output, price, and prots. Now assume the two rms form a cartel that produces the monopoly output for this market. The rms agree to share the cartel output and prot equally. (d) (5 points) What aggregate output will the cartel agree upon? What will be the market price and prot of each rm? (e) (5 points) Show why this cartel is not stable if the rms interact only once. What is each rm's optimal deviation if the other rm chooses the cartel quantity? Now suppose that the cartel is expected to exist indenitely and rms discount future prots at rate 6 where O