A police department must conduct 100 interrogations every month. Interrogations can be done by friendly looking “good-cops”, who earn £20,000, or by scary looking “bad-cops”, who earn £40,000. Assume that both types of police can be hired quickly but take several months to fire. When graphing the two kinds of police officer, put “good-cops” on the vertical axis. (a) Write an equation showing the police department’s costs as a function of good-cops and bad-cops hired. Convert this budget constraint into the equation for a line that could be plotted on a graph, with the number of good-cops as a function of total costs and the number of bad-cops hired. (b) The production function for interrogations is Q = min{good-cop, bad-cop}. Show the police department’s hiring decision in a large, suitably labelled graph. How many of each is hired? What are the department’s costs? (c) The next year, the police department starts training good-cops how to be intimidating and bad-cops to be friendly. The training is successful and changes the production function for interrogations to: Q= 0.5*good-cop + 0.5*bad-cop Show the short- and long-run effects on the department’s hiring of good- and bad-cops in a large, suitably labelled graph. What is the effect on costs?
A police department must conduct 100 interrogations every month. Interrogations can
be done by friendly looking “good-cops”, who earn £20,000, or by scary looking
“bad-cops”, who earn £40,000. Assume that both types of police can be hired quickly
but take several months to fire. When graphing the two kinds of police officer, put
“good-cops” on the vertical axis.
(a) Write an equation showing the police department’s costs as a function of
good-cops and bad-cops hired. Convert this budget constraint into the equation
for a line that could be plotted on a graph, with the number of good-cops as a
function of total costs and the number of bad-cops hired.
(b) The production function for interrogations is
Q = min{good-cop, bad-cop}.
Show the police department’s hiring decision in a large, suitably labelled
graph. How many of each is hired? What are the department’s costs?
(c) The next year, the police department starts training good-cops how to be
intimidating and bad-cops to be friendly. The training is successful and
changes the production function for interrogations to:
Q= 0.5*good-cop + 0.5*bad-cop
Show the short- and long-run effects on the department’s hiring of good- and
bad-cops in a large, suitably labelled graph. What is the effect on costs?
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