Question $1[50$ points$]$

Consider the DMP search model studied in class with a job matching function given by

M $=$ eQ$1/2$A

$1/2$

$1.$ Let b $=0\mathrm{.}58,$ z $=1\mathrm{.}5,$ k $=0\mathrm{.}45,$ e $=0\mathrm{.}955$ and a $=0\mathrm{.}5,$ where k is the cost of creating

a vacancy. The working age population is N $=1000,$ and labour force denote by Q$.$ As

standard in DMP model, we assume that consumers make their job search based on the

expected payoff he$/$she obtains from searching for work, EV $.$ Further, we assume that the

relationship between Q and EV $,$ which can be derived by maximizing the consumer$$s utility

is given by:

Q $=$ N

$($EV $$ b$)$

z $$ b

$($a$)$ Calculate market tightness j$.$ Show your calculation in details.

$($b$)$ What is the unemployment rate?

$($c$)$ What is the vacancy rate?

$($d$)$ Compute the expected payoff from the job search, EV$,$ and solve for the equilibrium

number of job searchers, Q$.$

$($e$)$ How many vacancies are posted in the economy? How many consumers are employed

in this economy? Calculate the aggregate output?

$($f$)$ Compute the equilibrium wage?

$2.$ Assume that the government sets the wage $10$ percent above its equilibrium value. What

will be the unemployment rate and how does it compare to the initial one? Using diagrams

explain how labour market tightness, j$,$ and labour force, Q are affected in the high wage

equilibrium.