Question

The quantity demanded of the commodity in the market is 25 units when the

selling price per unit is P12. Derive the demand equation given that because of the decrease

in price to P8 per units, the quantity demanded increased to 60 units.

Answer 1

$P_1=12,$ $Q_1=25$

$P_2=8,$ $Q_2=60$

order pairs (25,12) and (60,8) demand equation

$a=a-bp$

here b is slope., a is intercept

$slope=\frac{8-12}{60-25}\\=\frac{-4}{35}\\=-0.11$

Taking pairs to check demand equation, as we know demand equation is linear.

so,

$Y=mx+b\to linear\space equation$

where b is intercept in this and m is slope.

take (25,12)

$12=-0.11(25)+b\\b=12+2.85\\b=14.85$

Recheck this value take other order pair

take (60,8)

$8=-0.11(60)+b\\b=8+6.85\\b=14.85\to intercept$

Now

demand equation is

$Q=a-bp$

in tis a is intercept and b is slope

$Q=14.85-0.11P\to Demand\space equation.$