# Tag Info

Accepted

• 1,924

### Has mathematical economics contributed to the mathematics of space exploration?

In the history of dynamic programming some economic works are considered pioneering contributions to the theory of dynamic programming (and in this sense it can be said that they contributed to ...
• 4,047
Accepted

### What is the result of the Bellman Equation

...the result of applying sup operator is a NUMBER... Read it carefully. The equation is $$v(x_0) = \sup_{ \{x_t \}_{t \geq 1}} \cdots \quad (1)$$ This defines a function $v$, called the value ...
• 2,619

### Preference for consumption smoothing and actual smoothing

The argument relayed in the question as regards consumption smoothing is flawed. Consumption smoothing does not mean consumption equality over periods, but rather, tendency to avoid corner solutions, ...
• 33.9k

### Good book/article that goes into depth about transversality conditions?

A textbook on dynamic optimization which treats transversality conditions at some length is Chiang Elements of Dynamic Optimization. See especially sections 7.2 - 7.4 and 9.1.
• 8,529

The Euler Equation typically refers to the interior optimal choice between consumption today and tomorrow (or some similar intertemporal choice). That is, it equalizes the marginal utility of ...
• 31
Accepted

### How can I formulate the following optimization problem?

If you want to determine how much carbon dioxide should be omitted by solving an optimization problem, then a constraint on the quantity of $CO_2$ isn't quite what you need. The normal constraint on ...
• 8,529
Accepted

### Saddle path equilibrium on financial market with rational expectations

Suppose you have a dynamic system $$x_{t+1} = Ax_{t}$$ with a stationary point (or steady state as used in growth or RBC literature), say, $x^*$, i.e. $x^{*} = Ax^{*}$. Now, consider the following ...

### Good book/article that goes into depth about transversality conditions?

I think that references in this field can be of interest and useful also at distance of time from the original question. Transversality conditions are a complex subject in calculus of variations and ...
• 4,047

### Solving a HJB with a probability to transit to a new state

I would leave this as a comment but I cant. You are on the right track. Once you know $V_2(k)$ then you can plug that into to the first hjb and solve. To solve for $V_2$ you need to find the optimal ...
• 151
Accepted

### What is meant by the abbreviation 'MSV solution', used in the context of DSGE modeling?

Minimum state variable (MSV) solution is a special technique used to find an unique equilibrium with desirable properties in DSGE models. Often DSGE models can have multiple paths that will satisfy ...
• 57.2k
Accepted

### What is the difference between a perfect foresight equilibrium and a rational expections equilibrium?

This is not a formal definition, but a useful piece of intuition. I think that the best way to think about it is that when there is uncertainty in a model it arises mainly in two forms either there ...
• 4,188
Accepted

### Are overlapping generation (OLG) models extensions of a DSGE model?

You can find OLG models that do not classify as DSGE (in particular, the model might not be stochastic) as well as DSGE with overlapping generations (contrary to those with infinitely lived agents). ...
• 862

### Introduction of an asset tax in the AK model

I think your math is mostly correct but I have to admit that I am not used to AK models. A short answer for your main question: is it ok to introduce taxation in the model without including the ...
• 1,916
Accepted

### Resolution - Ramsey growth model with per capita variables

The reason why the $e^{nt}$ term is there is because you want to multiply the whole utility by the number of people. You are actually not substituting consumption into the utility but multiplying the ...
• 57.2k
Your maximization problem is $$\max_{x_1,x_2} x_1 \cdot (300 - 2x_1) + x_2 \cdot (200-1.25x_2) - x_1 - x_2$$ subject to $x_1 + x_2 \leq \overline{x}$ where $\overline{x}$ denotes the budget. The ...
Hi: Using the lag operator, L, for $y_t$, you can write $y_{t+1}(1- 5L) = 2 \longrightarrow y_{t+1} = \frac{2}{(1-5L)}$. But you cannot write that an an infinite series because the thing multiplying ...