1. Let’s assume that both the demand and supply are linear functions with respect to price. More

explicitly, let D(p)=4 - p and S(p)= 1+ p. Find a general solution for the price as a function of

time (it will involve k). What is the long term behaviour of the price? Does it tend to a specific value

regardless of the initial price?

Community Answer

【General guidance】The answer provided below has been developed in a clear step by step manner.Step1/1If any doubt please comment me,I will help youAnswer:-To find the general solution for the price as a function of time, we need to set the demand equal to the supply and solve for p:\( \begin{align*} &= \mathrm{{D}{\left({p}\right)}={S}{\left({p}\right)}}\\[3pt] &= \mathrm{{4}-{p}={1}+{p}}\\[3pt] &= \mathrm{{2}{p}={3}}\\[3pt] &= \mathrm{{p}=\frac{{3}}{{2}}} \end{align*} \)So the equilibrium price is \( \begin{align*} &= \mathrm{{p}=\frac{{3}}{{2}}} \end{align*} \)This means that in the long term, the price will tend towards 3/2 regardless of t ... See the full answer