A police department must conduct 100 interrogations every month. Interrogations can be done by friendly looking “good-co

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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?