# Market impact function

I have the following Dynamical system for market impact function

$$p_{t+1}-p_t=a(d_t-s_t)$$

$$s_{t+1}-s_t=bp_ts_t-cs_t$$ $$d_t=y-rp_t$$

where $$s_t$$ is quantity supplied, $$d_t$$ is quantity demanded, $$p_t$$ is market price, $$a,b,c,y,r>0$$ are fixed.

What is the name of the model? And most importantly,how can I interpret these equations?

Thanks

## 1 Answer

This is some dynamic supply-demand model (I am not aware of it having some special name).

The first equation gives you the evolution of prices. It says that there will be inflation if there is excess demand $$d_t>s_t$$ and deflation if there is excess supply (that’s why the first equation has ($$d_t-s_t$$).

The second equation tells you how supply changes in response to price in time. It is basically a dynamic version of basic supply curve. If the prices increase supply increases as well

The third equation is a demand function. The $$y$$ is most likely income - hence higher income the higher demand, and then the demand is decreasing in price

• Thank you. Well, which book should I read in order to understand deeply? – B11b Jan 6 '20 at 15:57
• @B11b I think Varians Microeconomic analysis is a good start, although I am not 100% sure if it includes also this exact same model I think the insights from the book can be directly applied to understand this kind of model. I wish I could recommend something more direct but nothing comes to mind maybe someone else will provide better reference – 1muflon1 Jan 6 '20 at 16:51