Question

In: Economics

Quantity Price 182 1.25 201 1.09 176 1.34 142 1.47 231 0.99 254 0.91 202 1.02...

Quantity Price
182 1.25
201 1.09
176 1.34
142 1.47
231 0.99
254 0.91
202 1.02
183 1.13
172 1.27
252 0.87
223 0.93
A. Given the Quantity and Price information above, estimate the linear demand equation by treating Quantity as the dependent variable.
B. Given your answer to part A, determine the inverse demand equation.  

This is the whole question, there is nothing in the question that is not visible.


what do you mean? the 2nd column is labled price.

Solutions

Expert Solution

We have the following information

Quantity (Q)

Price (P)

q = (Q - Mean)

p = (P - Mean)

q2

p2

qp

182

1.25

     -19.64

         0.13

      385.59

         0.02

       -2.64

201

1.09

       -0.64

       -0.03

           0.40

         0.00

         0.02

176

1.34

     -25.64

         0.22

      657.22

         0.05

       -5.76

142

1.47

     -59.64

         0.35

   3,556.50

         0.13

     -21.14

231

0.99

       29.36

       -0.13

      862.22

         0.02

       -3.68

254

0.91

       52.36

       -0.21

   2,741.95

         0.04

     -10.76

202

1.02

         0.36

       -0.10

           0.13

         0.01

       -0.03

183

1.13

     -18.64

         0.01

      347.31

         0.00

       -0.27

172

1.27

     -29.64

         0.15

      878.31

         0.02

       -4.58

252

0.87

       50.36

       -0.25

   2,536.50

         0.06

     -12.36

223

0.93

       21.36

       -0.19

      456.40

         0.03

       -3.96

2,218.00

       12.27

         0.00

         0.00

12,422.55

         0.38

     -65.18

ΣQ

ΣP

Σq

Σp

Σq2

Σp2

Σqp

Total observations (N) = 11

Mean of Quantity = ΣQ/N = 2,218.00/11 = 201.64

Mean of Price = ΣP/N = 12.27/11 = 1.12

Regression equation of Q on P: (Q – Mean of Q) = regression coefficient × (P – Mean of P)

Regression coefficient = Σqp/Σp2 = – 65.18/0.38 = – 171.53

(Q – Mean of Q) = regression coefficient × (P – Mean of P)

(Q – 201.64) = – 171.53 × (P – 1.12)

(Q – 201.64) = – 171.53P + 191.33

Q = 201.64 + 191.33 – 171.53P

Q = 392.97 – 171.53P (Linear Demand Equation)

Inverse demand equation:

Q = 392.97 – 171.53P

171.53P = 392.97 – Q

P = 2.29 – 0.01Q (Inverse Demand Equation)


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