Question

In a certain market for sobolo,when the price of the drink was Ghc 3 the quantity demanded was 12bottles.On another day,when the price per bottle was 5 cedis,the quantity demanded was 6 bottles.Use the information to write the equation for demand.Now,what will be quantity demanded if price per bottle was 6cedis.If we restrict price to the same demand curve,what will happen if price is less than Ghc 2.

Answer 1

Given;

(1). The formula to find the equation of demand is given below:

Q=a+mP

Where,

Q=Quantity demanded

a=x−intercept

$m=slope=\frac{Q_2-Q_1}{P_2-P_1}$

p=price

$slope=\frac{6-12}{5-3}=\frac{-6}{2}=-3$

$Q=a+(-3)p\\Q=a-3p\\$

substitute Q=12 and p=3 for a

$12=a-3\times3\\12=a-9\\a=12+9=21\\$

The demand equation is given below

$Q=21-3p$

(2)

If P=6 cedis then the quantity demanded will be as given below:

Q=21−3×6

Q=21−18

Q=3 bottles

At 6cedis 3 bottles will be demanded.

(3).

Note: This part is not clear as it has not mentioned what factor to consider.

If the price is less than Ghc 2 then the quantity demanded will increase and it will be high.

Q=21−3P

Or,

3P=21−Q

$p=\frac{21}{3}-\frac{Q}{3}\\p=7-\frac{Q}{3}$

If p<2

$7-\frac{Q}{3}<2\\7-2<\frac{Q}{3}\\5<\frac{Q}{3}\\15<Q$

If the price is less than 2 then the quantity demanded will be greater than 15 (but less than equal to 21 as the price can not be negative).