You are a manager in a large hotel chain that is about to open a hotel in a new city.You have been asked to determine the nightly rates that should be charged to the two distinct groups of customers that will stay at this hotel:tourists and business travelers.You can separate (and so identify) members of each group based on advanced booking.Therefore, you plan to implement third-degree price discrimination.To help you determine the profit-maximizing price for each group, you use a sample of data you have on these same groups of customers for the hotel chain in 50 other cities (these data can be found below).Based on prior research, you know that demand for both groups exhibit constant elasticity.Therefore, in using the data below, you will assume an exponential demand function, of the form:Q = APn, where Q is output (number of nightly stays per month), P is price per night, A is a constant, and "n" is the (constant) price elasticity of demand.

Part I:For each group of customers, run a regression to estimate "n," the price elasticity of demand for that group.(4 pts.)

NOTE:Since this is an exponential function, you will have to first transform the data into natural logs in order to estimate a linear regression of the form:

LN(Q) = LN(A) + nLN(P).

In this form, the estimated coefficient for the log of P (i.e. "n") will be, in fact, your estimate of the price elasticity of demand for that group.ALSO, because "n" is the price elasticity of demand, you should obtain a negative value from your regression and not omit the minus sign as you do calculations.

Part II:Use the results of your regressions to answer the question (determining the profit-maximizing price for each group).

HINT:Look at Slide 9 of the lecture notes.

NOTE:Assume marginal cost for each nightly stay is $40.

a.Based on your regression results, enter a formula in the respective boxes below to calculate the profit-maximizing price for each group of customers. (6 pts.)

After I have run the natural logs for the data and run a regression, how do I use this info to find the product maximizing price?

SUMMARY OUTPUT Regression Statistics Multiple R 0.966257 Q=11.4679*P^(-1.2688) R Square 0.933653 Adjusted R Square 0.932271 Standard Error 0.032327 Observations 50 ANOVA df SS MS F Significance F Regression 1 0.705887 0.705887 675.4733 6.26613E-30 Residual 48 0.050161 0.001045 Total 49 0.756048 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 11.46787 0.262168 43.74248 2.47E-40 10.94074701 11.99499 10.94075 11.99499439 Price T -1.2688 0.048819 -25.9899 6.27E-30 -1.366952404 -1.17064 -1.36695 -1.17063865