Demand, revenue, cost & profit

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Intros
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Lessons
  1. Demand, Revenue, Cost & Profit Overview:
  2. Demand functions
  3. Revenue functions
  4. Cost functions
  5. Profit functions
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Examples
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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?
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      Topic Notes
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      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)
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