Only two heating contractors offer to install geothermal heating systems in residential houses in Kingston: Brian and Kevin. Brian uses only high-quality pipes for the heating systems (which are buried in front of the house to absorb the geothermal energy from the ground). Installing a heating system using only high-quality pipes costs Brian $22,000. Kevin, on the other hand, uses only low- quality pipes, so installing a heating system costs him only $16,000. If customers were able to observe the quality of the pipes, they would pay $28,000 for a high- quality heating system, and only $20,000 for a low-quality heating system. However, customers cannot tell whether the heating contractor used high-quality or low-quality pipes. They only know that there is a 50-50 chance of getting high-quality pipes when randomly selecting a heating contractor. Assume that all customers are risk neutral. Moreover, assume that Brian would never consider using low-quality pipes for his heating systems (i.e., he would rather stop selling geothermal heating systems than using low-quality pipes). Note: Please round your final numbers to 2 decimal places. a) If the customers are not able to tell high-quality and low-quality heating systems apart, how much on average would they be willing to pay for the installation of a geothermal heating system (assuming they randomly choose one of the two heating contractors)? Does adverse selection occur? Briefly explain. (4 points) b) Brian considers offering a warranty for his high-quality geothermal heating systems. The cost of providing warranty is Cp = $600Y for Brian, and Cx = $1,000Y for Kevin, where Y is the length of the warranty (measured in years). Can Brian offer a warranty which is a credible signal of high quality? If so, what is the optimal length of this warranty? (6 points) c) What is the maximum length of the warranty so that it is optimal for Brian to offer the warranty? (4 points) d) Suppose the government now requires all heating contractors to offer a seven-year warranty for geothermal heating systems. (i) Given your answer to part (c), do we have a separating or a pooling equilibrium in Kingston when the government requires a seven-year warranty? Briefly explain. (ii) What is Brian's profit given the required seven-year warranty? Does adverse selection occur? Briefly explain. (6 points)