Boardwalk Inc. has the following demand function and total cost (TC) relationshi
ID: 1139592 • Letter: B
Question
Boardwalk Inc. has the following demand function and total cost (TC) relationship:
q = 300 - 0.5P + 10r + 4Y
where q is Boardwalk's product (sold at a per unit price equal to P), r is the price of a good related to q, and Y denotes income of Boardwalk's customers.
1. Is the related good a substitute or complement to Boadwalk's product? Explain.
For the remainder of problem #7 you can assume that the current value of r = 20 and Y = 25 .
2. Derive Boadwalk's inverse demand curve.
3. Determine the total revenue maximizing levels of output (q) and price (P).
Explanation / Answer
The demand function is q = 300 - 0.5P + 10r + 4Y
1. The related good is a substitute to Boadwalk's product. This can be confirmed from the sign of price coefficient of r, +10 which indicates that if price of related good is increased, the quantity demanded of Boadwalk's product will rise.
The current value of r = 20 and Y = 25 .
2. Boadwalk's demand curve is q = 300 - 0.5P + 10*20 + 4*25 = 600 - 0.5P
Inverse demand function is 0.5P = 600 - q or P = 600/0.5 - q/0.5. This gives P = 1200 - 2q.
3. Total revenue is Price x Quantity so TR = (1200 - 2q)*q or TR = 1200q - 2q^2
TR is maximized when MR is 0
MR = derivative of TR = 1200 - 4q. Hence we have 1200 - 4q = 0 which gives q = 1200/4 = 300 units. Hence total revenue maximizing levels of output (q) is 300 units and price (P) is 1200 - 2*300 = $600 per unit.