# 2. Suppose that pharmaceutical sales representative i derives utility from his/her job according to the utility function U;(W, T) = W -B(T – T/)?, where W denotes annual salary, T

2. Suppose that pharmaceutical sales representative i derives utility from his/her job
according to the utility function U;(W, T) = W -B(T – T/)?, where W denotes
annual salary, T E [0,1] is the fraction of annual work days spent away from
home, B > 0 is a taste parameter, and T7 is sales representative i’s preferred
fraction of annual work days spent travelling. Suppose that sales reps have
heterogeneous preferences for on-the-job travel; in particular, suppose that T, is
uniformly distributed on the [0,1] interval in the sales rep population.
On the demand side of the pharmaceutical sales rep labor market, suppose that a
fixed fraction p of jobs require "low travel", T = Tz, and a fixed fraction 1 -p of
jobs require "high travel", T = TH, where 0 S TI < TH = 1.
a. Illustrate the typical sales rep’s indifference curves in the T-W plane.
b. Explain in words what condition must hold if a particular pair of salaries,
(WL, W#) – one for "low travel" jobs and one for "high travel" jobs – is
an equilibrium.
c. Express the condition in (b) as an equation. (nt: Given worker
preferences, which sales representative must be indifferent between the
two jobs?)
d. Manipulate the equation in (c) to obtain an expression for the equilibrium
salary differential between "high travel" and "low travel" jobs, WH – WL,
as a function of the parameters {8, p, TL, T#). Is the equilibrium
compensating differential unambiguously signed?
e. Determine how a ceteris paribus change in each of the parameters affects
the equilibrium compensating differential, and interpret your results. The question is in the image that I linked.

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