For Town H and Town W determine whether the price charged last year was above, below or equal to the profit-maximizing price. (After receiving questions from a few students, we would like to clarify that Question 4 of your first assignment is referring to the profit maximizing price for the same number of memberships sold last year in the two towns.)
Using the same number of memberships sold last year in the two towns and assuming the marginal cost is 0 as per the notes provided in the assignment, the price charged was found to be the following:
Your regression output is correct. Now you have Q = a -bP +cM + dN you have average values of M and N that you multiply by the c and d values you've created with the regression output and get an equation of the form Q = A - bP where (A = a +cM +d N)
That give you a demand equation of which you take the inverse and get P = A -bQ which is multiplied through by Q since PQ = TR that allows you to take the derivative and obtain an MR curve. Since MC = 0 in this situation you find the optimum price by setting the MR you obtained above equal to zero and you have your optimum price.
Known:
Town H
|
Demand (Q)
|
Price (P)
|
Income (M)
|
Population (N)
|
Revenue (TR)
|
Fixed cost (MC)
|
Profit (MR)
|
|
Town H
|
3309
|
$ 58
|
$ 41,000
|
28000
|
$ 191,922
|
$ 78,000
|
$ 113,922
|