Ajax Limited and Brutus, LLC. are the only suppliers of services that calibrate the send/receive GPS tracking equipment on trucks that are used by various trucking companies to monitor their shipping assets within the Midwest. No other suppliers have the equipment necessary to perform these calibrations. The market inverse demand for these services is given below.

Q=8,000-100P

where P is price per treatment and Q is total number of calibrations per month.For simplicity, also assume that both firms have fixed costs of $500 per month at each location. From company records, you are given the following variable cost function for each firm:

TVC_A=32Q_A+0.04Q²_A and TVC_B=20Q_B+0.02²_B

In the work that follows, use 3 decimal places for your calculations, but you may round all your results to 2 decimal places to reduce the clutter in your answers.

a.Suppose The Flash is contemplating buying both companies and since Brutus has lower operating costs, his first thought is to shut down Ajax and supply the entire market as a single plant monopoly. If he does this, what price will he charge per calibration and how many calibrations will he sell each month? What profits will he expect to earn?

b.Flash has second thoughts about shutting down Ajax. If he decides to go ahead with the purchase and keep Ajax in operation, he will have to operate the firm as a multiplant monopoly. If he decides to go ahead and buy the two firms, what price will he charge per calibration and how many calibrations will he sell each month? What profits will he expect to earn? How many calibrations will be performed by each operation?

c.After careful consideration, Flash decides that he isn't interested in buying the two companies after all. In this case the market reverts back to a two-firm Cournot duopoly. Calculate the Cournot market equilibrium price-output solutions for each firm including their respective profits.

d.Summarize the results of your findings over the three possible outcomes. In your summary include price, quantity and industry profits. Comment on your results.