The inverse market demand for a certain good is: P=1002Q, where Q is the industry output. There are two symmetric firms producing the good, each with the following cost function: TCi=10qi, where qi is the output of the i th firm (i=1,2). (a) Suppose that the firms are competing in quantities. If someone produces more than their share of the cartel output, the other firm punishes them by reverting to the Cournot output. What is the critical value of the discount factor ? (b) Now assume that the detection lag (the time required to discover and respond to cheating) is two periods. What is the critical value of the discount factor ? (c) Now assume that the firms with the above cost functions compete in prices (without capacity constraint). If someone produces more than their share of the cartel output, the other firm punishes them by reverting to the Bertrand equilibrium. What is the critical value of the discount factor ? (d) In which of the above cases is cartel formation most likely? The inverse market demand for a certain good is: P=1002Q, where Q is the industry output. There are two symmetric firms producing the good, each with the following cost function: TCi=10qi, where qi is the output of the i th firm (i=1,2). (a) Suppose that the firms are competing in quantities. If someone produces more than their share of the cartel output, the other firm punishes them by reverting to the Cournot output. What is the critical value of the discount factor ? (b) Now assume that the detection lag (the time required to discover and respond to cheating) is two periods. What is the critical value of the discount factor ? (c) Now assume that the firms with the above cost functions compete in prices (without capacity constraint). If someone produces more than their share of the cartel output, the other firm punishes them by reverting to the Bertrand equilibrium. What is the critical value of the discount factor ? (d) In which of the above cases is cartel formation most likely