Answer in Microeconomics for taha #173368

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%.

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}{0.5cdot(4000+2000)}}{dfrac{$1.0-$1.5}{0.5cdot($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=-1.5cdot4.5%=-6.75%.”

Therefore, the demand will decrease by 6.75%.