Answer to Question #294897 in Economics of Enterprise for B blessed

Question

Supply and demand conditions can be expresses in quadratic form. Find the price and quantity given;

The demand function; p+q²+3q-20=0

The supply function; 3q²+10q= 5.

From your answer a above determine what happen when government decides to fix price;

a. Above the equilibrium price

b. Below the equilibrium price

[Hint; hypothetical diagram is essential]

Answer 1

To Find Price and Quantity

Demand: $P+q^2+3q-20=0$

$P=20-q^2-3q$

Supply: $3q^2+10q=5$

$3q^2+10q-5=0$

We have to begin with the quadratic solving of the P value first in the demand equation.

$ax^2+bx+c=0$

$-q^2-3q+20=0$

$\frac{-3^2 \mp \sqrt(-3^2-4\times-1\times 20)}{-2}$

$\frac{9\mp9.43}{-2}$

$x=-9.22$ $\to not\ economically\ viable$

$\bold{x=0.217}$ $\to equal\ to\ P$

now we replace the value of P in the equation to make it solvable alongside the supply function.

$P=20-q^2-3q$

$0.217=20-q^2-3q$

$q^2+3q-19.783=0$

$3q^2+10q-5=0$

we equate the like demand and supply functions to get;

$3q^2-q^2+10q-3q-5+19.783=0$

$2q^2+7q+14.783=0$

solving quadratic equation we get;

$\frac{-7^2 \mp \sqrt(-7^2-4\times 2\times 14.785)}{4}$

$\frac{49 \mp \sqrt(167.26)}{4}$

$\bold{q}=9$

Above Equilibrium Price

At a higher than equilibrium price, quantity demanded reduces, as the amounts suppliers are willing to offer for the price increase. Due to the deficit in demand for products already in the market, forces of demand and supply forces price down to the point where such supply equates to demand.

Below Equilibrium Price

Below the equilibrium price, the price floor leads to the increased demand that exceeds available goods in the market. eventually, the deficit in supply will pull back prices to the equilibrium level where demand equals supply.