Question

315 Elasticity Practice with different demand curves

Please show ALL work.

1) Q = 75 – 5P                       find elasticity at P = 3 (or between $2.50 and $3.50)

2)   Q = 75 – 5P                      find elasticity at P = 5 (or between $4.50 and $5.50)

3) Q = 42 – 6P                                    find elasticity at P = 3 (or between $2.50 and $3.50)

4) Q = 42 – 6P                       find elasticity at P = 5 (or between ($4.50 and $5.50)

5) P = 28 – 4Q                                    find elasticity at P = 3 (or between $2.50 and $3.50)

6) P = 28 – 4Q                                    find elasticity at P = 5 (or between $4.50 and $5.50)

7) Q = 84 – 7P                                    what is the price so that elasticity = -1?

8) Q = 80 – 6P                                    what is the price so that elasticity = -1?

9) P = 4 – 0.2Q                       find elasticity at P = 3 (or between $2.50 and $3.50)

10) P = 4 – 0.2Q                     find elasticity at P = 5 (or between $4.50 and $5.50)

11) Q = 20 – 5P                      find elasticity at P = 3 (or between $2.50 and $3.50)

12) Q = 20 – 5P                      find elasticity at P = 5 (or between $4.50 and $5.50)

Answer 1

Elasticity of Demand = (-1/Slope) ( P / Q)

1) Q = 75 - 5P

Elasticity at P =3

Q = 75 - 5(3)

Q = 75 - 15

Q = 60

(P,Q) = (3,60)

Inverse demand = (1/5)Q = 15 - P

P = 15 - (1/5)Q

Slope = -(1/5)

Elasticity = [-1 / (-1/5)] [3 / 60]

              = 5 * 0.05

              = 0.25

2) Q= 75 - 5P

Elasticity at P = 5

Q = 75 - 5(5)

Q = 75 - 25

Q = 50

(P,Q) = (5 , 50)

we know slope = -(1/5)

Elasticity = [-1 / (-1/5)] [5 / 50]

               = 5 * 0.1

               = 0.5

3) Q = 42 - 6P

Elasticity at P = 3

Q = 42 - 6(3)

Q = 42 - 18

Q = 24

(P,Q) = (3,24)

Inverse demand = (1/6)Q = 7 - P

P = 7 - (1/6)Q

Slope = -(1/6)

Elasticity = [-1 / (-1/6)] [3 / 24]

               = 6 * 0.125

                = 0.75

4) Q = 42 - 6P

Elasticity at P = 5

Q = 42 - 6(5)

Q = 42 - 30

Q = 12

We know slope = -(1/6)

Elasticity = [-1 / (-1/6)] [5 / 12]

               = 6 * 0.4167

               = 2.5

5) P = 28 - 4Q

Here it is a inverse demand function, therefore slope = -4

Elasticity at P = 3

3 = 28 - 4(Q)

4Q = 25

Q = 6.25

(P,Q) = (3,6.25)

Elasticity = [-1 / (-4)] [3 / 6.25]

               = 0.25 * 0.48

               = 0.12

6) P = 28 - 4Q

We know slope = -4

Elasticity at P = 5

5 = 28 - 4Q

4Q = 23

Q = 5.75

(P,Q) = (5,5.75)

Elasticity = [-1 / -4] [5 / 5.75]

               = 0.25 * 0.8696

               = 0.2174