Question

Consider the quantities supplied of fanny packs at two different prices for three different time horizons:

Time	P0 (Initial Price)	P1 (New Price)	Q0 (Initial Price)	Q1 (New Quantity)
Time A	10	12	50	70
Time B	10	12	50	55
Time C	10	12	50	40

(a) (i) Calculate the price elasticity of supply of fanny packs for Time A.

(ii) Is the supply of fanny packs at Time A perfectly inelastic, inelastic, unit elastic, elastic, or perfectly

elastic?

(b) (i) Calculate the price elasticity of supply of fanny packs for Time B.

(ii) Is the supply of fanny packs at Time B perfectly inelastic, inelastic, unit elastic, elastic, or perfectly

elastic?

(c) (i) Calculate the price elasticity of supply of fanny packs for Time C.

(ii) Is the supply of fanny packs at Time C perfectly inelastic, inelastic, unit elastic, elastic, or perfectly

elastic?

(d) Based on your solutions to Parts (a), (b), (c), which time horizon would expect to represent the shortest amount of time? Time A, Time B, or Time C? Explain your answer in your own words.

(e) Based on your solutions to Parts (a), (b), (c), which time horizon would expect to represent the longest amount of time? Time A, Time B, or Time C? Explain your answer in your own words.

Answer 1

Time period A

Price elasticity of demand (PED)= % change in quantity demanded /% change in price of the good.

        % change in quantity demanded = ((New quantity-old quantity)/old quantity)) x 100

Initial quantity (q₀) =50    Initial price (p₀)= $ 10

New quantity (q₁)= 70   New price (p₁) $ 12

% change in quantity demanded = ((New quantity-old quantity)/old quantity)) x 100

% change in quantity demanded= ((70-50)/50)) x100

                                                         =( 20/50) x100

                                                       = 40%

            

% change in price = ((New price-old price)/old price)) x 100

% change in price= ((12-10)/10)) x100

                                                         =( 2/10) x100

                                                       = 20%

Price elasticity of demand = 40/20= 2

PED is elastic as it is >1.

Time B

Initial quantity (q₀) =50    Initial price (p₀)= $ 10

New quantity (q₁)= 55   New price (p₁) $ 12

% change in quantity demanded = ((New quantity-old quantity)/old quantity)) x 100

% change in quantity demanded= ((55-50)/50)) x100

                                                         =( 5/50) x100

                                                       = 10%

            

% change in price = ((New price-old price)/old price)) x 100

% change in price= ((12-10)/10)) x100

                                                         =( 2/10) x100

                                                       = 20%

Price elasticity of demand = 10/20= 0.5

PED is inelastic as PED < 1.

Time C

Initial quantity (q₀) =50    Initial price (p₀)= $ 10

New quantity (q₁)= 40   New price (p₁) $ 12

% change in quantity demanded = ((New quantity-old quantity)/old quantity)) x 100

% change in quantity demanded= ((40-50)/50)) x100

                                                         =( 10/50) x100

                                                       = 20%

            

% change in price = ((New price-old price)/old price)) x 100

% change in price= ((12-10)/10)) x100

                                                         =( 2/10) x100

                                                       = 20%

Price elasticity of demand = 20/20= 1

PED = 1, so it is unit elastic.