Work the following exercise. (See Examples 1 – 4.)Suppose that the demand and price for a...

Work the following exercise. (See Examples 1 – 4.)

Suppose that the demand and price for a certain brand of shampoo are related by

where p is price in dollars and q is demand. Find the price for a demand of

(a) 0 units;

(b) 4 units;

(c) 8 units.

Find the demand for the shampoo at a price of

(d) $6;

(e) $11;

(f) $16.

(g) Graph p = 16 - (5/4)q.

Suppose the price and supply of the shampoo are related by

where q represents the supply and p the price. Find the supply when the price is

(h) $0;

(i) $10;

(j) $20.

(k) Graph p = (3/4)q on the same axes used for part (g).

(l) Find the equilibrium quantity.

(m) Find the equilibrium price.

Example 1

Joseph Nolan has studied the supply and demand for aluminum siding and has determined that the price per unit, * p, and the quantity demanded, q, are related by the linear equation

Example 2

Suppose the economist in Example 8 concludes that the supply q of siding is related to its price p by the equation

Example 3

The supply and demand curves of Examples 8 and 9 are shown in Figure 3.22 . Determine graphically whether there is a surplus or a shortage of supply at a price of $40 per unit.

Example 4

In the situation described in Examples 8 – 10, what is the equilibrium quantity? What is the equilibrium price?