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lOMoARcPSD|69091439 PART 1 (2 marks) EverKleen Pool Services provides weekly pool maintenance in Atlanta. Dozens of firms provide this service. Services are standardized (->perfect competition); each company cleans the tank and ensures the suitable chemical levels in the water. Services are usually provided with a four-month summer contract. The market price for a four-month summer service contract is $115. EverKleen Pool Services has fixed costs of $3,500. EverKleen managers estimate the marginal cost function for the firm as follows, using data from the past two years: SMC = 125 – 0.42Q + 0.0021Q2; where SMC is in dollars and Q is the number of pools serviced each summer. Each estimated coefficient is statistically significant at the 5% level. Question 1.1: Should EverKleen continue to operate, or should it close? (1 mark) AVC=125-0.21Q+0.0007Q^2 Maximize profit: MR=MC=P=> 125 – 0.42Q + 0.0021Q^2=115=> Q1= 172, Q2=27 Q = 27 => AVC = 119.84 > P (Loại) Q=172=>AVC=109.5888 < P = 115 => Firm should operate at Q = 172 C2: TC = 125Q -0.21Q^2 + 0.0007Q^3 + 3500 → TVC = 125Q -0.21Q^2 + 0.0007Q^3 → AVC = 125 - 0.21Q + 0.0007Q^2 AVCmin in case AVC = SMC → 125 - 0.21Q + 0.0007Q^2 = 125 – 0.42Q + 0.0021Q^2 → Q = 150 → AVC min = 109.25 P > AVC min (115 > 109.25) → Firm should continue to operate Question 1.2 : How much profit (or loss) can EverKleen Pool Services expect? (1 mark) profit = 115*Q - (125*Q - 0.21*Q^2 + 0.0007*Q^3 + 3500) Q = 172 → profit = -2569.2736 => Firm experiences a loss of $2569.2736 C2: TC = 125Q -0.21Q^2 + 0.0007Q^3 + 3500 → ATC = 125 - 0.21Q + 0.0007Q^2 + 3500/Q = 132.58 Loss = (P - ATC) * Q = (115 - 132.58)*150 = -2637 EverKleen Pool Services can expect a loss at -2637 $ Downloaded by Hai Phan Chinh (haiphanchinh34@gmail.com) lOMoARcPSD|69091439 PART 3 (4 marks) : In EverKleen, there are two people: The employee (Raquel) and the employer (Vera). Raquel has to choose whether to pursue training that costs $Z to herself or not. Vera has to decide whether to pay a fixed wage of $W (Z and W are given by yourself, W > Z) to Raquel or share the revenues of the enterprise 50:50 with Raquel. The output is positively affected by both training and revenue sharing. Indeed, with no training and a fixed wage total output is $20,000, while if either training or profit sharing is implemented the output rises to $22,000. If both training and revenue sharing are implemented the output is $25,000. Question 3.1: Construct the pay-off matrix (2 marks) Z = 2000 W = 4000 Vera (employer) Raquel (employee) Fixed wage Share revenue Training 22000 - 4000 = 18000 25000 / 2 = 12500 No Training 20000 - 4000 = 16000 22000 / 2 = 11000 Vera Raquel Fixed wage Share revenue Training 4000 - 2000 = 2000 25000 / 2 - 2000 = 10500 No Training 4000 22000 / 2 = 11000 Vera Raquel Fixed wage Share revenue Training 2000 | 18000 10500 | 12500 No Training 4000 | 16000 11000 | 11000 Question 3.2: Is there any equilibrium in dominant strategies? Why or Why not? (1 mark) Dominant strategies of Raquel is No Training Dominant strategies of Vera is Fixed wage Downloaded by Hai Phan Chinh (haiphanchinh34@gmail.com) lOMoARcPSD|69091439 → There is an equilibrium in dominant strategies at {Rachel: No training; Vera: Fixed wage}. Because both Vera and Raquel have dominant strategies. Question 3.3: Is there any Nash equilibrium? Why or Why not? (1 mark) Nash equilibrium is {Rachel: No training; Vera: Fixed wage}. Because both Raquel and Vera don’t want to deviate from this equilibrium Downloaded by Hai Phan Chinh (haiphanchinh34@gmail.com)