The economy produces a final good Yt that can be used as: Intermediate good xt as input. The input for innovation; research spending, Rt. Consumption good: Ct. So the resources constraint in the economy is this one:

In each period, there is a fixed number of individuals L, each of whom lives for a period and is endowed with a unit of labor services that they offer inelastically. Their utility depends only on their consumption and they’re risk-neutral, so their objective is to maximize

The final good Yt is produced in perfect competition using the inputs Work=L and intermediate good xt through this Cobb-Douglas function: The intermediate product is produced by one monopolist in each period such that for every intermediate product unit used, he/she uses one

The quality of intermediate good, At, is the result of innovation, that is costly and uncertain. Each period, the entrepreneur tries to innovate. If his try is successful, the quality increases with respect to the last period. Otherwise, it stays the same as before, At-1. The

The model has the next steps: 0: Period t starts with productivity At-1 inherited from last period. 1: The entrepreneur investors in research choosing his effort in this investment, Rt. 2: The innovation is successful or unsuccessful, and productivity At evolves accordingly.

Solving the model, we get to this investment in research adjusted for productivity n=(Rt/At*), this probability of success in the innovation and this growth rate. This is clearly an endogenous growth model. We see that the growth rate increases with lambda. This reflects the

This is very interesting, but we may wonder: Is this result socially efficient? It turns out the answer is NO: Let’s suppose we have a social planner whose objective is to maximise GDPt. We solve for backwards induction again.

We get that in the social optimum the production of the intermediate good and the final good are higher than in the decentralised equilibrium. We also get an expression for the price of the intermediate product.

What about the probability of success? It’s higher in the social optimum if and only if:

So in this economic, we have two distortions: Monopoly distortion: Governed by the parameter alpha in the price. The lower the alpha, the higher the price. It determines the equilibrium mark-up. Innovation externality: The entrepreneur only takes into account the success

According to these equations, an increase in population leads to an increase in growth. This has been challenged by empirical evidence by C. Jones (1995b), as the authors acknowledge. Aghion and Howitt deal with it incorporating A. Young’s (1998) insight that “as population

In this thread I have used a simplified discrete model based on theirs. You can find the original one here: Aghion, P., & Howitt, P. (1992) https://www.jstor.org/stable/2... And also greatly explained by the authors in their book ‘The Economics of Growth’: https://mitpress.mit.edu/97802...

I hope you have enjoyed this thread as much as I have enjoyed writing it. I will upload more Economics threads soon. Have a good day!

If you liked this thread, you might like this thread about a model by Aghion and Howitt that explains how we can achieve environmentally sustainable economic growth🌱

@FranNunesEcon Jefe!!

@VonMoff ¡Muchísimas gracias!

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@CarlosRamirezF Muchas gracias, Carlos

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