Question

4. The only thing that changes in Dullsville is the price of a stay at the Dullsville Inn. You've collected the following data on the rates charged (for a suite with 2 queen-sized beds and 'free' continental breakfast) and the number of rooms occupied. The Inn has 100 suites, and at no time were potential visitors turned away due to no vacancy. Use this data to estimate a 'constant elasticity' demand function. Estimate the price elasticity of demand.                                                                                                                     

                Observation          Rate per night       Quantity (rooms rented)                   

                1              $70         40                          

                2              $65         50                          

                3              $80         30                          

                4              $52         62                          

                5              $92         31                          

                6              $64         41                          

                7              $43         78                          

                8              $74         35                          

                9              $83         33                          

                10           $54         52                          

                11           $87         30                          

                12           $84         28                          

                13           $68         40                          

                14           $43         69                          

                15           $48         53                          

                16           $78         34                          

                17           $72         48                          

                18           $58         53                          

                19           $56         59      

Answer 1

In order to estimate the price elasticity of demand, estimate the log-log model for the demand schedule.

The log-log model is of the form:

LN(Q) = b0 + b1*LN(P)

Where, Q=Quantity (rooms rented) and P = Rate per night  

The regression result is:

The "constant elasticity" demand function is:

LN(Q) = 8.92875587425359 -1.23381840673702*LN(P)

The slope coefficient of LN(P) is the constant price elasticity of demand

Hence, the price elasticity of demand is -1.23381840673702