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ECON3430: MANAGERIAL ECONOMICS
Problem Set 1 (15%) Due: Monday, April 5th, 2021 at 4pm.
Questions
For all questions, make (and state) your own assumptions if a good answer requires additional
information.
1) Jim is a salesperson at the DM paper company. The utility function of Jim is given by
u(w, b, e) = w + b − c(e) where w ∈ ℝ is Jim′ s weekly wage, b is a bonus payment that is
conditional on sales revenue, and c(e) is Jim′s cost of effort where c(e) = 1 if e < 10 and c(e) = (
12 × (e − 10) 2) if e ≥ 10.
Michael is Jim’s boss, who is maximising DM’s profits which are given by: π (w, b, e) = R(e) −
w − b, where R(e) is the firm′s sales revenues and R(e) = 100e Michael cannot observe Jim’s
effort (e) directly but observes R(e) and can set the bonus level dependent on sales revenues.
a. If Michael sets w=100 and b=0, what would be Jim’s effort level (e) and DM’s
profits? (1 mark)
Solution
Jim’s effort level
Bonus, b depends on sales revenue, R (e)
Assumption: b is directly proportional to R (e)
Therefore, if b = 0, R (e) = 0
Since R (e) = 100e
0 = 100e
Thus, Jim’s effort level, e = 0
DM’s profits, π
π (w, b, e) = R(e) − w – b
π =...