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)