Consider the general demand function:

Q_d = 8,000 - 16P + 0.75M + 30P_R

a. Derive the equation for the demand function when M = $30,000 and P_R = $50.

b. Interpret the intercept and slope parameters of the demand function derived in part a.

c. Sketch a graph of the demand function in part a. Where does the demand function intersect the quantity-demanded axis? Where does it intersect the price axis?

d. Using the demand function from part a, calculate the quantity demanded when the price of the good is $1,000 and when the price is $1,500.

e. Derive the inverse of the demand function in part a. Using the inverse demand function, calculate the demand price for 24,000 units of the good. Give an interpretation of this demand price.