Midterm control

Example 4
Let demand and supply functions be in the form D(t)  4  4 p(t), S(t)  8  4 p(t 1). Find the formula for the price p(t) and the supply and demand quantity for an arbitrary t when the initial price is p0 = 4
Solution.
Using the condition of equality of supply and demand at the equilibrium point, we can write the equation 4-4p(t) = 8-4p(t-1). This results in the recurrent equation p(t) = -1-p(t1).



A recurring formula is created. It can be seen that over time price fluctuations occur with a frequency equal to 4.5 units from the equilibrium value. The formula for demand is as follows:

And for the supply, it will look like this