Question

Grannyâs Restaurant sells apple pies. Granny knows that the demand curve for her pies does not shift over time, but she wants to learn more about that demand. She has tested the market for her pies by charging different prices. When she charges $4 per pie, she sells 30 pies per week. When she charges $5, she sells 24 pies per week. If she charges $4.50, she sells 27 apple pies per week.
a. Is the apple pie market perfectly competitive? Why or why not?

b. With this data, draw a graph of the linear demand curve for Grannyâs apple pies.

c. Find the price elasticity of demand at each of of the three prices.

Answer 1

Answer:

A. Apple Pie Market Not perfectly competitive

B. Demand Curve Equation : q = 8.84 - 0.16p

C. Price Elasticity of Demand : 0.8 , 1.25

Explanation:

A. The Apple pie market is not perfectly competitive because the perfectly competitive market has large no of buyers & sellers, the demand is perfectly inelastic (infinite demand at given constant prices). However in this market , apple pie demand (sales) are responding to price change , so its not perfectly competitive

B. Demand curve is the graphical representation of price, demand. The Demand curve function : q = a - bp ;  where q = quantity, p = price, a = autonomous demand , b = represents price demand relationship & is negative because of negative price demand relationship (Law of Demand).

Putting q & p given values : 4 = a - 30b ; 5 = a - 24 b. Solving these two equations for a & b , we get : a = 8.84 , b = 0.16 . So, the demand curve equation becomes : q = 8.84 - 0.16p  & plotting this equation , we get demand curve.

C. Price Elasticity of Demand is responsiveness of demand to price change. Formula : %change in demand/ %change in price =  ∆Q /∆P X P/Q

P    Q

4    30  (*)

5    24  (**)

4.5   27 (***)

Ped (*, **) =  ∆Q /∆P X P/Q =  (6 / 1) x (4/30) = 0.8

Ped (*, **) =  (3 / 0.5) x (4/30) = 0.8

Ped (**, ***) = (3 / 0.5) x (5/24) = 1.25