ECON 428/528 Assignment 4

ASSIGNMENT > ECON 428/528 Assignment 4

Nazarbayev University ECON 428 Nazarbayev University ECON 428 ECON 428/528 Assignment 5 – Deadline: Friday, April 21, 2023 at 6:00 pm Note: Write substantive answers, in whatever style you consider the most effective: do not try to fill in space with aimless speculation. The grading function is symmetric and additively separable over ...[Show More]

Nazarbayev University
ECON 428
Nazarbayev University
ECON 428
ECON 428/528 Assignment 5 – Deadline: Friday, April 21, 2023 at 6:00 pm

Note: Write substantive answers, in whatever style you consider the most effective: do not try to fill

in space with aimless speculation. The grading function is symmetric and additively separable over

questions, and it is convex. You are expected to upload your answers as a single file to Moodle.

Important: Feel free to discuss questions with each other, but you are NOT allowed to solve them

together. Making same mistakes in a similar order will be judged as plagiarism that will not be

tolerated and be sanctioned according to the Student’s Code of Misconduct. You need to write down

your own original answers and submit them to Moodle as a single file. You can use a software (ex:

Word or Latex) to type your answers, or scan your handwritten answers into a pdf file. In the latter

case, you are responsible for the quality of scanning. Late submissions are NOT accepted!

1. True/False/Uncertain: Analyze the following assertion and state whether it is true, false, or

uncertain. Explain your reasoning shortly (a couple of sentences should easily suffice):

a. [Spring 2022 FINAL] "If the cost of monitoring effort falls for a firm, the efficiency

wage will decrease."

b. "The bonding critique criticizes the model of efficiency wages because profit-maximizing

firms should never be willing to pay more than the competitive wage."

2. Efficiency Wage: Consider a simple efficiency wage model. A worker’s utility as a function of

wages w and effort e is given by u(w,e). The worker’s effort level can take on only 2 levels,

e∈ {0,´ e } . The firm’s monitoring activity is such that with probability γ, the worker will be

monitored. In this case, if the worker is shirking, she is fired. If the worker is not monitored

(happens with probability 1-γ), the worker is not fired regardless of effort choice. Given that the

firm offers wage w, the worker’s expected utility if she chooses not to shirk is given by

E (u (w , e´ ))=ln ( w)-´ e . If she chooses to shirk, her expected utility is

E (u (w ,0))=(1-γ ) ln (w )+γ [u ln (b )+(1-u) (ln ( w^ )-´ e)] , where b is unemployment benefits,

w^ is the market wage and u is the unemployment level. Denote by ~w the minimum

incentive compatible wage that the firm will set to ensure that worker will choose not to shirk. In

equilibrium without shirking it must be that ~w=w^ . Suppose γ = 0.5, b = 1, e´=1/13 , and

the equilibrium market wage is w^ = 7.389. What must the equilibrium unemployment rate be?

(Note that ln(7.389) = 2.)