In the town of Inksville, Tats for Tots (i.e., TFT) is the only tattoo parlor de
ID: 1196936 • Letter: I
Question
In the town of Inksville, Tats for Tots (i.e., TFT) is the only tattoo parlor dedicated to the under-18 age group. Being a monopolist, TFT hires you to advise it on the best price and quantity of tattoos to sell each month. You estimate the following inverse monthly market demand for tattoos:
P = 1000 - Q,
where P is the price charged per tattoo and Q is the overall quantity of tattoos produced and sold each month. You also estimate the monthly total cost (TC) for TFT, given by the following:
TC = 20,000 + 200•Q.
Determine the values of P and Q which maximize TFT’s profit. What is TFT’s profit at these optimal values of P and Q?
Explanation / Answer
P = 1000 - Q; TC = 20,000 + 200•Q.
MR = 1000-2Q; TR = 1000 - Q^2
TC = 20,000 + 200*Q
MC = 200*2Q; MC=400Q
MR=1000-2Q = 2Q=MC: 1000 = 4Q
Q = 250.
P=1000-Q, and so P=1000-250 = $750
TR = 1000Q - Q^2 = 250,000 - 62,500 = $187,500.
TC = TC = 20,000 + 200•Q; 20,000 + (200*250)
TC = 20,000 + 50,000 = $70,000
Profit = TR - TC = 187,500 - 70,000 = $117,500.
*****