Question

Insurance Price	Number of Customers
$900	5
$800	10
$700	20
$600	35

1. Calculate the point price elasticity of demand for health insurance when price decreases from $900 to $600. (10pts)
2. Calculate the point price elasticity of demand for health insurance when price increases from $600 to $900. (10pts)
3. Using the mid-point formula, calculate the price elasticity of demand for Blue Cross-Blue shield health insurance, when its price increases from $600 to $900, and decreases from $900 to $600.  If you got a different result from a) or b) above, explain why. (20pts)

PLEASE SHOW ALL YOUR WORK

Answer 1

As per the information provided in the question

(A)when the price for health insurance (P) decrease from $900 to $600, its number of customer (Q) increases from 5 to 35

P1 =$900                              Q1=5

P2=$600                               Q2=35

∆P=P2-P1= 600-900 =-300

∆Q=Q2-Q1 =35-5 =30

As per the point method of estimation of price elasticity of demand (Ep)

Ep=(∆Q/∆P)x(P1/Q1)

Ep=(30/-300)x(900/5)= -18

Ep= 18   (More elastic)

The negative sign indicates that insurance is a normal good

since Ep= 18 >1, therefore, it is more elastic

(B) when the price for health insurance (P) increases from $600 to $900, its number of customer (Q) decreases from 35 to 5

P1 =$600                              Q1=35

P2=$900                               Q2=5

∆P=P2-P1= 900-600 =300

∆Q=Q2-Q1 =5-35 =-30

As per the point method of estimation of price elasticity of demand (Ep)

Ep=(∆Q/∆P)x(P1/Q1)

Ep=(-30/300)x(600/35)= -1.714

Ep= 1.714

The negative sign indicates that insurance is a normal good

since Ep= 1.714 >1, therefore, it is more elastic

(C)when the price for health insurance (P) increases from $600 to $900, its number of customer (Q) decreases from 35 to 5

P1 =$600                              Q1=35

P2=$900                               Q2=5

∆P=P2-P1= 900-600 =300

∆Q=Q2-Q1 =5-35 =-30

Price elasticity of demand (Ep) using mid-point method is = ∆Q/∆P x [{(P1+P2)/2}/{(Q1+Q2)/2}]

Ep= -30/300 x [{(600+900)/2}/{(35+5)/2}]

Ep= -30/300 x (750/20) = -3.75

Ep=3.75

The negative sign indicates that insurance is a normal good

since Ep= 3.75 >1, therefore, it is more elastic

(D)when the price for health insurance (P) decrease from $900 to $600, its number of customer (Q) increases from 5 to 35

P1 =$900                              Q1=5

P2=$600                               Q2=35

∆P=P2-P1= 600-900 =-300

∆Q=Q2-Q1 =35-5 =30

Price elasticity of demand (Ep) using mid-point method is = ∆Q/∆P x [{(P1+P2)/2}/{(Q1+Q2)/2}]

Ep= 30/-300 x [{(900+600)/2}/{(5+35)/2}]

Ep= 30/-300 x (750/20) = -3.75

Ep=3.75

The negative sign indicates that insurance is a normal good

since Ep= 3.75 >1, therefore, it is more elastic

(E) Comparison between Solution A and Solution B

the price elasticity as per (solution A) is Ep=18

the price elasticity as per (solution B) is Ep=1.714

since in solution A and B we have used point method of estimation of price elasticity of demand, where the change in price and change in quantity are same but the base price and base quantity are not same in different solution.

Comparison between Solution C and Solution D

the price elasticity as per (solution C) is Ep=3.75

the price elasticity as per (solution D) is Ep=3.75

since in solution C and D we have used mid-point method of estimation of price elasticity of demand, where the change in price and change in quantity are same and the average of base and new price and average of base and new quantity are same in different solution. As a result the estimated answer in both the solution are same

Comparison between methods (Point Method and Mid-point method)

in the solution A and B we have used the point method of estimation of price elasticity of demand where the ratio of change in quantity and price is multiplied with the base price and base quantity.

Ep=(∆Q/∆P)x(P1/Q1)

With the change in the increase and decrease in price in the given problems the change in price and change in quantity are same but the base price and base quantity are not same in different solution

in the solution C and D we have used the mid-point method of estimation of price elasticity of demand where the ratio of change in quantity and price is multiplied with the average of base and new price and average of base and new quantity.

(Ep) = ∆Q/∆P x [{(P1+P2)/2}/{(Q1+Q2)/2}]

where the change in price and change in quantity are same and the average of base and new price and average of base and new quantity are same in different solution. As a result the estimated answer in both the solution are same