Finding the linear demand function

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SUMMARY

The discussion focuses on deriving the linear demand function for a resort hotel based on booking data. Given that 50 rooms are booked at $100 per night and 80 rooms at $80, the demand function can be established using the point-slope formula. The correct approach involves plotting the points on a graph and applying the linear equation format to find the relationship between price and quantity. This analysis ultimately leads to determining the optimal price for maximizing revenue.

PREREQUISITES
  • Understanding of linear equations and functions
  • Familiarity with the point-slope formula in algebra
  • Basic knowledge of revenue maximization concepts
  • Ability to interpret graphical data
NEXT STEPS
  • Learn how to apply the point-slope formula in linear demand functions
  • Study revenue maximization techniques in economics
  • Explore graphical representation of demand curves
  • Investigate the impact of price elasticity on demand
USEFUL FOR

This discussion is beneficial for economics students, hotel managers, and anyone interested in understanding demand functions and revenue optimization strategies.

cinematic
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Homework Statement


The manager of a 120-room resort hotel has found that, on average, 50 rooms are booked when the price is $100 per night and 80 rooms are booked when the price is $80 per night. Find the demand function, assuming that it is linear, and what price should he charge to maximize revenue?


Homework Equations


So I thought of it as two linear equations, but I don't understand how to obtain the demand function. Is it 100=50-x and 80=80-x? Doesn't seem right to me...


The Attempt at a Solution


Sadly, all the other questions involve a single price, and I don't know how to work with two. Any help would be awesome!
 
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Hey!

Draw a figure with price on the vertical axis and output on the horizontal axis. Plot the points from the problem. You'll notice that you have four points, you can use the point slope formula to construct your demand function

Good luck!
 
Last edited:

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