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I am seeking help with the Mortensen-Pissarides model in discrete time? Basically, I was given the following in class example (which we didn’t complete do to time constraints associated with the end of the semester).

Our workers Bellman Equations are as follows:

$V_u=b$$+\frac{aV_e+(1-a)V_u}{1+r}$ and

$V_e=$$w+\frac{\lambda V_u+(1-\lambda)V_e}{1+r}$ respectively

With $V_u$ and $V_e$ are expected utility values for unemployed and employed worker(s). a (∈ (0,1)) is the job-finding rate, b (> 0) is the unemployment benefits, r (> 0) is the real interest rate, w is the wage; and λ (∈ (0, 1)) is the job-destruction rate.

find the law of motion of the unemployment rate, given a and $\lambda$

Suppose that w is set to the reservation wage. Describe the condition that $V_u$ and $V_e$ must satisfy in this case. Then, given the values of b, a, λ, and r, compute the equilibrium values of $V_u$ and $V_e$.

My professor didn’t have time to explain this concept, but said it would be super important if we intend to take the next highest macro course my universities grad school offers. Essentially this is a solve for yourself equation for summer vacation, but I am lost. Can any one show me what to do?

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To get things started:

The reservation wage is the wage that makes the worker indifferent between taking a job and getting V_e and not taking a job and getting V_u. To find it, solve for the value of w that makes V_e = V_u.

Solving the entire model is not possible given the info you provided. You need the block that describes the firms.

My sense is that it would be most useful for you to read about the MP model and then post more specific questions based on a complete model. A good reference is Romer's Advanced Macro book.

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