Answer to Question #173368 in Microeconomics for taha

Question #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%.


1
Expert's answer
2021-03-23T08:23:06-0400

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


Ed=Q2Q10.5(Q2+Q1)P2P10.5(P2+P1),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)}},Ed=400020000.5(4000+2000)$1.0$1.50.5($1.0+$1.5)=1.67.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 Ed>1E_d>1, demand is elastic.

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


ϵ=PQdQdP,\epsilon=\dfrac{P}{Q}\dfrac{dQ}{dP},Q=50010P,dQdP=10,Q=500-10P, \dfrac{dQ}{dP}=-10,ϵ=P50010P(10)=PP50.\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:


ϵ=303050=1.5.\epsilon=\dfrac{30}{30-50}=-1.5.

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

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


Ed=%ΔQ%ΔP,E_d=\dfrac{\%\Delta Q}{\%\Delta P},%ΔQ=Ed%ΔP,\%\Delta Q=E_d\%\Delta P,%ΔQ=1.54.5%=6.75%.\%\Delta Q=-1.5\cdot4.5\%=-6.75\%.

Therefore, the demand will decrease by 6.75%.


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