Answer to Question #173368 in Microeconomics for taha

Question

A. Suppose you own a company that supplies vending machine. Currently , your vending machine sells soft drinks at $1.50 per bottle. At that price, customer purchase 2,000 bottles per week. In order to increase sales , you decide to decrease the price to $1.00 and sales increases to 4,000 bottles. Calculate price elasticity of demand.

         B. Suppose the demand curve for a product is given by  q=500-10p 

i.       Compute the price elasticity of this demand function.

ii.      What is price elasticity of demand when the price is $30?

iii.     What is the percentage change in demand if the price is $30 and increased by 4.5%.

Answer 1

A) The price elasticity of demand can be calculated as follows:

$$E_d=\dfrac{\dfrac{Q_2-Q_1}{0.5(Q_2+Q_1)}}{\dfrac{P_2-P_1}{0.5(P_2+P_1)}},$$ $$E_d=\dfrac{\dfrac{4000-2000}{0.5\cdot(4000+2000)}}{\dfrac{\$1.0-\$1.5}{0.5\cdot(\$1.0+\$1.5)}}=-1.67.$$

Since $E_d>1$, demand is elastic.

B) i) We can find the price elasticity of demand as follows:

$$\epsilon=\dfrac{P}{Q}\dfrac{dQ}{dP},$$ $$Q=500-10P, \dfrac{dQ}{dP}=-10,$$ $$\epsilon=\dfrac{P}{500-10P}\cdot(-10)=\dfrac{P}{P-50}.$$

ii) Let's find the price elasticity of demand when the price is $30:

$$\epsilon=\dfrac{30}{30-50}=-1.5.$$

Since $\epsilon >1$ the demand is elastic.

iii) By the definition of the price elasticity of demand, we have:

$$E_d=\dfrac{\%\Delta Q}{\%\Delta P},$$ $$\%\Delta Q=E_d\%\Delta P,$$ $$\%\Delta Q=-1.5\cdot4.5\%=-6.75\%.$$

Therefore, the demand will decrease by 6.75%.