Question

Supply and demand for a product are both a linear function of price. Suppose that if a price of $8 is charged, 8 units will be demanded; that if a price of $5 is charged, 20 units will be demanded; that if a price of $3 is charged, 38 units will be supplied; and that if a price of $1 is charged, 26 units will be supplied. For what price will supply equal demand?

Answer 1

Answer:

At $2 supply and demand are in equilibrium for 32 quantity

Explanation:

We have to solve for the linear equation first, and then calcualte the equilibrium price and quantity

$m = \frac{y_1- y_2}{x_1-x_2}$

Demand

$\left[\begin{array}{cc}x&y&5&20&8&8\end{array}\right]$

$m = \frac{20- 8}{5-8} = 12\div -3 = -4$

Then we solve for h

$20 = -4\times5 + h \\ 20+20 = h \\h = 40$

Demand would be y = -4x +40

We repeat the process with supply

$\left[\begin{array}{cc}x&y&1&26&3&38\end{array}\right]$

$m = \frac{38- 26}{3-1} = 12\div 2 = 6$

$38 = 6\times3 + h \\ 38 -18 = h \\h = 20$

Supply is y = 6x + 20

Now we can solve for equilibrium price

$\left \{ {{y = -4x +40} \atop {y = 6x + 20}} \right.$

-4x + 40 = 6x + 20

20 = 10x

x = 20/ 10 = 2 price

And quantity

6 x 2 + 20 = 32

-4x2 + 40 =  32