Demand, revenue, cost & profit

Demand, revenue, cost & profit

Lessons

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)
  • Introduction
    Demand, Revenue, Cost & Profit Overview:
    a)
    Demand functions

    b)
    Revenue functions

    c)
    Cost functions

    d)
    Profit functions


  • 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.
    a)
    Find the demand function p(q)p(q)

    b)
    Find the revenue function R=R(q) R=R(q)

    c)
    Find the cost function C=C(q) C=C(q)

    d)
    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.
    a)
    Find the demand function p(q)p(q)

    b)
    Find the revenue function R=R(q) R=R(q)

    c)
    Find the cost function C=C(q) C=C(q)

    d)
    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?

  • 4.
    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?