Question 3: Cooltown is an unbearably cold place in the winter. One of the unfortunate consequences of the cold weather is that low-income residents, who cannot afford to spend very much on clothing, suffer disproportionately during the winter. In response to their discomfort, the mayor institutes a new program under which every city resident is entitled to one warm coat (with a store value of $100) that can be obtained from an official in City Hall. Individuals must personally collect their winter coats. Since the winter is quite cold, a large number of people are likely to want free coats. Even people who do not need new coats might be tempted to get one at City Hall, since individuals can sell their coats to the local store for $100 each. a) Consider the case of an econ major financial analyst who earns $200 per hour. The analyst considers the length of the coat line (assumed to be known) before deciding whether or not to get a coat. Under what conditions will the analyst decide to get a coat? What is the effective price the analyst pays to obtain the coat? b) The analyst earns the top wage in Cooltown. Assume that there are 200 residents in Cooltown, each of whom earns different wages ranging from $1/hour to $200/hour. (That is, one person earns $1/hour, one person earns $2/hour, one person earns $3/hour, and so on, up to the analyst who earns $200/hour.) The mayor's social media account reports that the line for coats is always the same length: one must stand in line for H hours. Which people will decide to stand in line for coats? Graph the value of a coat, and its effective price, as a function of the private sector wage of the potential coat recipient. Your graph should have the private sector wage on the horizontal axis and $ on the vertical axis. c) Now suppose that H is a simple function of the number of people standing in line: H=N/4, in which N is the number of people who line up for coats this winter. What is the equilibrium length of the coat line? Which people decide to obtain coats? What are their net benefits (that is, the benefit of a coat minus the effective price of a coat)? [Hint: The marginal person will be just indifferent between the option of waiting in line and getting a coat and the option of skipping out on the whole thing. Because of the set-up of the problem, that person's wage will be equal to N, the number of people who wait in line.] d) The welfare system is often criticized for stigmatizing low-income people, by making them wait in line at welfare offices and endure various other indignities). Is there a function served by making people wait in line for income assistance? Is such a system efficient or inefficient? Question 3: Cooltown is an unbearably cold place in the winter. One of the unfortunate consequences of the cold weather is that low-income residents, who cannot afford to spend very much on clothing, suffer disproportionately during the winter. In response to their discomfort, the mayor institutes a new program under which every city resident is entitled to one warm coat (with a store value of $100) that can be obtained from an official in City Hall. Individuals must personally collect their winter coats. Since the winter is quite cold, a large number of people are likely to want free coats. Even people who do not need new coats might be tempted to get one at City Hall, since individuals can sell their coats to the local store for $100 each. a) Consider the case of an econ major financial analyst who earns $200 per hour. The analyst considers the length of the coat line (assumed to be known) before deciding whether or not to get a coat. Under what conditions will the analyst decide to get a coat? What is the effective price the analyst pays to obtain the coat? b) The analyst earns the top wage in Cooltown. Assume that there are 200 residents in Cooltown, each of whom earns different wages ranging from $1/hour to $200/hour. (That is, one person earns $1/hour, one person earns $2/hour, one person earns $3/hour, and so on, up to the analyst who earns $200/hour.) The mayor's social media account reports that the line for coats is always the same length: one must stand in line for H hours. Which people will decide to stand in line for coats? Graph the value of a coat, and its effective price, as a function of the private sector wage of the potential coat recipient. Your graph should have the private sector wage on the horizontal axis and $ on the vertical axis. c) Now suppose that H is a simple function of the number of people standing in line: H=N/4, in which N is the number of people who line up for coats this winter. What is the equilibrium length of the coat line? Which people decide to obtain coats? What are their net benefits (that is, the benefit of a coat minus the effective price of a coat)? [Hint: The marginal person will be just indifferent between the option of waiting in line and getting a coat and the option of skipping out on the whole thing. Because of the set-up of the problem, that person's wage will be equal to N, the number of people who wait in line.] d) The welfare system is often criticized for stigmatizing low-income people, by making them wait in line at welfare offices and endure various other indignities). Is there a function served by making people wait in line for income assistance? Is such a system efficient or inefficient
