Question

2) An economist believes there is a linear relationship between the market price p of a particular
commodity and the number of suppliers are willing to bring to the market place. Two sample
observations indicate that when the price equals $15 per unit, the weekly supply equals 30,000
units and when the price is $20 per unit the weekly supply is 48000 units.
i) If price p is plotted on the horizontal axis and the quantity supplied q is on vertical axis. Graph the
linear equation.
ii) Identify and interpret the meanings of slope p and q intercepts.
iii) Predict the weekly supply if the market price equals $35 per unit.

Answer 1

Solution.

i)  If price p is plotted on the horizontal axis and the quantity supplied q is on vertical axis then the graph will be a line passing through the points with coordinates (15;30000) and (20;48000).

ii)The equation of the line has the form: $y=kx+b$ were $k=tan\alpha.$

Find $k$ and $b$ from the system of equations

$\begin{cases} 30000=15k+b\\ 48000=20k+b \end{cases};$

$\begin{cases} 48000=20k+b \\ 30000=15k+b \end{cases} -;$

$18000=5k;$

$k=3600;$ $tan\alpha=3600;$

$30000=15\sdot3600+b \implies b=-24000;$

$q=3600p-24000 -$ equation of this graph;

iii)If $p=35$ $ then $q=3600\sdot35-24000=102000$ units;

Answer:If p=35 $ then 102000 units.