What is the profit maximising ticket price, Managerial Economics

A promoter decides to rent an arena for concert. Arena seats 20,000. Rental fee is 10,000. (This is a fixed cost.) The arena owner gets concessions and parking and pays all other expenses related to concert. The promoter has properly estimated the demand for concert seats to be Q = 40,000 - 2000P, where Q is the quantity of seats and P is the price per seat. What is the profit maximising ticket price?

As the promoter's marginal costs are zero, promoter maximises profits by charging a ticket price which will maximise revenue. Total revenue equals price, P, times quantity. Total revenue is represented as a function of quantity, so we need to work with the inverse demand curve:

P (Q) = 20 - Q / 2000

This gives total revenue as a function of quantity, TR (Q) = P (Q) x Q, or

TR (Q) = 20Q - Q2 / 2000

Total revenue reaches its maximum value when marginal revenue is zero. Marginalrevenue is first derivative of total revenue function: MR (Q) =TR'(Q). So

MR (Q) = 20 - Q / 1000

Setting MR (Q) = 0 we get

0 = 20 - Q / 1000

Q = 20,000

Recall that price is a function of quantity sold (inverse demand curve. So to sell this quantity, ticket price should be

P (20000) = 20 - 20,000 / 2,000 = 10

It may appear more natural to view the decision as price setting instead of quantity setting. Normally, this isn't a more natural mathematical formulation of profit maximisation since costs are generally a function of quantity (not of price). In this specific illustration, though, the promoter's marginal costs are zero. This means the promoter maximises profits simply by charging a ticket price that would maximise revenue. In this specific case, we characterise total revenue as a function of price:

TR2 (P) = (40,000 - 2000P)P = 40,000P - 2000 (P) 2

Total revenue reaches its maximum value when marginal revenue is zero. Marginal revenue is the first derivative of the total revenue function. So

MR2 (P) = 40,000 - 4000P

Setting MR2 = 0 we get,

0 = 40,000 - 4000P

P = 10

Profit = TR2 (P) -TC

Profit = [40,000P - 2000(P) 2] - 10,000

Profit = [40,000(10) - 2000(10)2] - 10,000

Profit = 400,000 - 200,000 - 10,000

Profit = 190,000

What, if the promoter had charged 12 per ticket?

Q = 40,000 - 2000P.

Q = 40,000 - 2000(12)

Q = 40,000 - 24,000 = 16,000 (tickets sold)

Profits at 12:

Q = 16,000(12) = 192,000 - 10,000 = 182,000

Posted Date: 8/12/2013 2:43:57 AM | Location : United States







Related Discussions:- What is the profit maximising ticket price, Assignment Help, Ask Question on What is the profit maximising ticket price, Get Answer, Expert's Help, What is the profit maximising ticket price Discussions

Write discussion on What is the profit maximising ticket price
Your posts are moderated
Related Questions

Economics is generally defined as the problem of how best to allocate limited resources, limited because needs are characterized as unlimited, but common sense tells us that rather

what is the goal of firm

Function of Money Markets The money markets are the place where money is "wholesaled".  As such the supply of money and interest rate which are of significance to the whole ec

How does economic theory contribute to managerial decisions

explain williamsons model of managerial discretion?

I was given a few spreadsheets and asked to do an income, balance and cash flow statement. It''s a lot of info and I have no idea what I''m doing

Q. Time Factor for Determinants of Demand? Price-elasticity of demand depends moreover on the time that consumers take to adjust to a new price: longer the time taken, greater


The demand curve Suppose that starting from a condition of equilibrium, the price of X falls relative to Y.  We now have a condition where the utility from the last shilling s