# Tag Info

5

As already commented, the equation you probably meant is $$\rho V(k)= \sup_c \{\, u(c) + V'(k) ( f(k) -\delta k -c ) \,\}.$$ I have never seen this equation called the HJB equation (probably missing a basic reference on my part). I'll call it "dynamic programming PDE". What you're really asking is the connection between two approaches to solve ...

4

No. Consider the following problem: Each period, one total unit of consumption falls from the sky that can be distributed between the two agents in any way. Their per-period utility is simply how much they consume. We let $\alpha=1/2$. Assume that $\beta_1>\beta_2$; the first agent is more patient. All optimal allocations have a very simple form: The ...

4

It is meant in a way that these models are highly influential and many papers are based on them. From my own experience it is impossible to attend macroeconomic conference without having couple of papers that are based on models of overlapping generations or on neoclassical growth model. The reason for that is that the models are quite useful and easily ...

3

It would seem that the way you've formulated your production function/law of motion has introduced double counting into the problem. Note that substituting 1 and 2 into 3 gives: $$k_{t+1}=(1-\delta)(c_t+x_t)+x_t$$ Where investment in period t is counted twice. The correct law of motion is simply: $$3. \: k_{t+1}=(1-\delta)x_t$$ And the general form of ...

2

No, they cannot by definition. To derive a time-invariant policy function, you need to have an infinite horizon problem. This is because the structure of the solution remains the same, no matter when you look at it. Intuitively, this is because any sequence of periods from any time period to infinity looks the same. The technical conditions for this can be ...

2

Your value function is as follows: $$V_t[w] = \max_{c_t \in[0,w]} \left\{u(c_t) + \frac{1}{2}V_{t+1}[\alpha(w_t - c_t)] + \frac{1}{2}V_{t+1}[\beta(w_t-c_t)] \right\}$$ with the terminal condition $$V_{T}[w_T] = \max_{c_T \in [0,w_T]} u(c_T)$$ So, we can solve this via backward induction. Clearly, at the final period $T$, since $u$ is monotonic, we ...

1

(The second equation for the value function of the unemployed should be $$v(w,U)= \max \{v(w,E); \,u[c,1]+\beta\int v(w', U) dF(w')\}. \quad (*)$$ ) ...how do you know when your problem solution require more than one Bellman equation? Whenever the state space of the problem contains discrete coordinates, there would be "multiple" value ...

Only top voted, non community-wiki answers of a minimum length are eligible