Question

Suppose the demand for petrol by an average motorist is given by the following demand equation: Q = 2000P^−k, where Q is litres purchased per year, P is the price in dollars per unit, and k is a parameter and equals (0.75) for the orange demand curve shown (attached). a) Calculate the quantity of petrol demanded by the average motorist if the price is $1.0 per litre.b) Suppose the price of petrol increases from $1.0to $2.0 per litre on a sustained basis. Calculate the change in quantity demanded.

Answer 1

Given

The demand equation is given

$Q=2000P^{-k}$

here Q is liters purchased per year, P is the price in dollars per unit and k is a parameter =0.75.

Explanation

a. To determine the quantity of petrol demanded by the average motorist if the price is 1 dollar per liter.

$\begin{gathered} Q=2000(1)^{-0.75} \\ Q=2000\text{ /year.} \end{gathered}$

b. To determine the change in quantity demanded.

It is given that the price of petrol increases from $1.0to $2.0 per litre on a sustained basis.

Then the equation becomes

$\begin{gathered} Q_1=2000(1)^{-0.75} \\ Q_2=2000(2)^{-0.75} \end{gathered}$

The change in quantity demanded is

$\Delta Q=\frac{Q_2-Q_1}{Q_1}$

Substitute the values.

$\begin{gathered} \Delta Q=\frac{1189.2-2000}{2000} \\ \Delta Q=-\frac{810.8}{2000} \\ \Delta Q=-0.4054 \end{gathered}$Answer

a.The quantity of petrol demanded by the average motorist if the price is 1 dollar per liter is 2000 litres per year.

b. The change in quantity demanded is the fall in demand due to negative sign which is 0.4054.