Demand, revenue, cost & profit

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. Demand, Revenue, Cost & Profit Overview:
  2. Demand functions
  3. Revenue functions
  4. Cost functions
  5. Profit functions
?
Examples
Lessons
  1. Finding the Demand, Revenue, Cost and Profit Functions
    Desmond's Laptop Company is selling laptops at a price of $400 each. They estimate that they would be able to sell 200 units. For every $10 dollars increase in price, the demand for the laptops will decrease 30 units. Assume that the fixed cost of production is $42500 and each laptop costs $50 to produce.
    1. Find the demand function p(q)p(q)
    2. Find the revenue function R=R(q) R=R(q)
    3. Find the cost function C=C(q) C=C(q)
    4. Find the profit function P(q) P(q) . What is the net profit if 100 units are sold?
  2. Patsy is selling phones at a price of $700 each. They estimate that they would be able to sell 1000 units. For every $1 dollars decrease in price, the demand for the phones will increase by 50 units. Assume that the fixed costs of production are $300000 and each phone costs $200 to produce.
    1. Find the demand function p(q)p(q)
    2. Find the revenue function R=R(q) R=R(q)
    3. Find the cost function C=C(q) C=C(q)
    4. Find the profit function P(q) P(q) . For what values of qq will we have a negative net profit?
  3. Break even points
    The demand and cost function for a certain company is:
    p=q+400p=-q+400
    C(q)=1000+19q2C(q)=1000+19q^2
    For what value(s) of qq causes you to have a profit of zero?
    1. The demand and cost function for a certain company is:
      p=9q2p=\frac{9}{q^2}
      C(q)=6+3qC(q)=6+3q
      For what value(s) of qq causes you to have a profit of zero?
      Free to Join!
      StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
      • Easily See Your Progress

        We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
      • Make Use of Our Learning Aids

        Last Viewed
        Practice Accuracy
        Suggested Tasks

        Get quick access to the topic you're currently learning.

        See how well your practice sessions are going over time.

        Stay on track with our daily recommendations.

      • Earn Achievements as You Learn

        Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
      • Create and Customize Your Avatar

        Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
      Topic Notes
      ?
      Demand is the relationship between the price of an item and the number of units that will sell at that price. In other words,
      Demand →p(q) p(q)
      where p is the price and q is the number of quantity. Usually, p(q)p(q) is expressed as the equation
      p=mq+bp = mq+b

      Revenue is the amount of income a company makes. The revenue function is expressed as
      R=pqR=pq
      When you know what the demand is, then you can express RR as a function in terms of qq.

      Cost is the amount of money a company needs to produce the items they are selling. It is usually expressed as C(q)C(q).

      Profit is the net amount a company makes. It can be calculated by subtracting revenue from cost. In other words,
      P(q)=R(q)C(q)P(q)=R(q)-C(q)