Point Price Quantity demanded

A $2.00 400

B $2.50 375

C $3.00 350

D $3.50 325

E $4.00 300

 

 

a)      The market price for a doughnut was $3.00. However, it is now $3.50. Use the midpoint to calculate the price elasticity of demand ( ) for doughnuts.

b)     How sensitive is the quantity demanded for cupcakes to price changes? Please explain briefly.

c)      For this question use the price elasticity of demand calculated in part (a). If the price of doughnuts increases by 20%, how much will the quantity demanded change by?

Given that:

Point  Price Quantity demanded

A $2.00 400

B $2.50 375

C $3.00 350

D $3.50 325

E $4.00 300

Step-by-step explanation

Part A.

P1 = 3, P2 = 350

Q1 = 3.50, Q2 = 325

Mid-point method of Ed

=[(Q2-Q2)/(Q2+Q1/2)] / [(P2-P1)/(P2+P1/2)]

=[(Q2-Q1)/P2-P1)]*[(P2+P1) / (Q2+Q1)]

=[(325-350)/(3.50-3)]*(3.50+3)+(325+350)

=-162.5/337.5 = -0.4815 = -0.48

The price elasticity of demand = -0.48

Part B.

Quantity demanded will decrease by 0.48% when price increases by 1%

Ed = -0.48

|Ed| = 0.48<1

Quantity demanded is not too sensitive to change in price of cupcakes.

Part C.

Given that percentage change in price = 20%, therefore:

Ed = percentage change in Quantity demanded/percentage change in price

-0.48 =percentage change in Quantity demanded/20%

Percentage change in Quantity demanded = (-0.48*20%) =-9.6%

Therefore, quantity demanded will change by -9.6%