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 | ||||
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.
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)