# Questions tagged [dynamic-optimization]

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### Intertemporal profit maximization

Assume a producer wishes to maximize the net present value, choosing optimal quantities of K and L. variables are time dependent. y is the production function, p is the price of y. K is capital, r is ...
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1 vote
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### How to solve dynamic problem with 2 production functions?

Suppose we have the following problem: $\max \int_0^\infty \exp(-\rho t) u(c(t))dt$ where $c(t)$ is consumption at time $t$. Subject to: $\dot{k}(t)= f(k(t))- c(t) - \delta k(t)$. where $k$ is capital,...
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1 vote
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### Nonhomogeneous linear dynamic system exercise

I have the following system of equations: \begin{align*} x_{t+1} & = 3x_t + y_t \\ \\ y_{t+1} & = 2 + 5y_t. \end{align*} I know how to solve it when I do not have a constant, but I couldn't ...
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### Has mathematical economics contributed to the mathematics of space exploration?

We see the work of Bellman showing up in both orbital trajectory planning/optimization and, obviously DSGE modeling. Also, in a recent example, the JWST uses ideas surrounding Pareto optimization and ...
1 vote
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### Optimization Model for Market Clearing using Uniform Pricing

Dear all, can someone please share a simple example for market clearing via Uniform Pricing using an Optimization Model? I am trying to simulate a market using bid values with quantity and price, from ...
40 views

### 2 dimensional optimization using fminsearch

I have a complicated capital - debt capital structure optimization problem but to start off simple I just added an extra parameter to the stochastic neoclassical growth model to see how the ...
1 vote
33 views

### Utility maximization across yield curves?

I'm attempting to solve a utility maximization problem for return-on-investment (ROI) across two different products, where each product experiences a different linear ROI curve. For product one, the ...
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### Dynamic Information Provision model setup - It generalizes Dirk Bergemann and Stephen Morris

The following model setup is from the paper Dynamic Information Provision: Rewarding the Past and Guiding the Future by Ian Ball. It generalizes both the ideas of strategic information transmission of ...
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### Current best methods for solving dynamic optimization problems in high dimensional state spaces

I was wondering what the current best methods are for solving dynamic optimization problems in high dimensional state spaces. Let me lay out the common cases where I would do something like this in ...
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### dynamic macroeconomics: Does the system "state" affect the dynamic optimization problem?

I am new to economics, but come from a statistics and math background, so the control theory and dynamic optimization ideas are familiar to me. What is a little confusing is that in most control ...
• 385
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### What assumptions can be made to ensure convexity in this optimization problem?

This question is a continuation of the question I asked at: How can I show convexity of this value function? Where I came to the conclusion that more assumptions are required to show that the ...
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### How can I show convexity of this value function?

I have set up an optmization problem as follows: $$V(A)=\max_{l, C} \quad u(C,l)$$ Where the only constraint is as follows: $$C=f(l,A)$$ Here $u$ is the utility function which captures social welfare. ...
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### How can I formulate the following optimization problem?

I want to set up an optmiization problem for global warming in which a planner determines how much carbon dioxide gas is emitted. Let's say we reduce this problem down to two periods, then I ...
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### What is the 'fixed point problem'?

I understand what the fixed point is, but don't understand what the fixed point 'problem'. Is it resolved by 'fixed point iteration'? I am reading a paper, and the paper mentions that the default ...
72 views

### Necessary conditions in overlapping generations model (OLG)

The consumer at each period maximizes $$\displaystyle\sum_{i=1}^{I}\beta^{i-1}U(c^i_{t+i},l^i_{t+i}) , t=0,1,2,3,...$$ subject to (1+\eta_t)c^{i}_t+...
64 views

### More equations than endogenous variables in RBC model

I recently came across my late father's bachelor's thesis, in which a RBC model is described. It appears to be a variant of Hansen's 1985 model with indivisible labor. I wrote the model into Dynare to ...
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### Value function iteration with stochastic productivity's standard deviation

Hello I would like to know how would you discretize the AR(1) process of technology in a standart RBC model when there is stochastic productivity's standard deviation. Namely I have: Technology $Z_t$ ...
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### Neoclassical Two-Sector Model of Endogenous Growth: Getting the consumption growth rate

I'm struggling to derive the growth of consumption from a two-sector model with the traditional Cobb-Douglas function. The model I am speaking about incorporates the fractions used by physical and ...
1 vote
113 views

### reference request - dynamic discrete time optimization methods

Next semester I am taking business cycle theory course. I emailed my teacher and he replied that I need firm understanding of dynamic discrete time optimization methods. I am gonna study mainly from ...
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### Resolution - Ramsey growth model with per capita variables

Let's say that we have the sum of the utility of a social planner $$\int_{0}^{\infty}U\left(C\right)e^{-\rho t}dt$$ where $C$ is the total consumption. If we want to write this by a per capita ...
• 2,135
1 vote
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### Introduction of an asset tax in the AK model

Let's start by analyzing the family's problem with the imposition of a tax. Assuming a CRRA utility function: U = \int_0^\infty e^{-(\rho-n)t} \cdot \left[ \frac{c^{1-\theta}-1}{1-...
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### Optimization in discrete time

I have made optimizations in continuous time that belong to the control theory, for example one case: $\max(\min)V[u(t)]=\int_0^Tf(t,x(t),u(t))dt$ constraint to: $\dot x=g(t,x(t),u(t))$ Where: $x(t)$: ...
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### Can anyone help me understand the Motrtensen-Pissarides model?

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 ...
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1 vote
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### Solving a HJB with additional constraints on control and state variables

I am trying to solve a Hamiltonian-Jacobi-Bellman equation with additional constraints on the state and control variables, but I am a bit confused on how to do that. In Intrilligator 2002, it is ...
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### How to optimize this dynamical system? Needing guidelines

I'm trying to solve a growth model, where the author indicates is a dynamical system. I want to ask if someone would help me with some guidelines of how to optimize this, I've been trying to solve it ...
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