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# Economic
Concepts

### Cost, Revenue and Profit

The
following terms are used in discussing the production and sale of
a product.

1) The
*output* is to the number of units produced.

2) The
cost of producing a commodity depends on many factors.

a) Some
costs are incurred no matter what the output. These are the *fixed
costs*.* *

b) The*
variable cost *are those costs which vary with output.
For any given output, the* average variable cost* is
the variable cost divided by output.

c) The
*total cost* is the sum of the fixed cost and variable cost.

_{Total
Cost = Fixed Cost + (Average Variable Cost) x Output}

3) The
*total revenue* from the sale of a good is the selling price
multiplied by the number of units sold; this is the total income
from sales.

4) The
*profit* is the difference between revenue and cost,

Profit
= Revenue - Cost.

5) The
*break-even point* is the point where revenue equals cost,
or equivalently profit = 0. Production is profitable only
when revenue is greater than cost.

6) The
*average total cost,* (or, briefly, average cost) is the total
cost divided by output,

_{}.

#### Example 1

If the fixed costs are
$100 if the average variable cost is $2, and if the selling price
is $2.50 per unit then:

a) the
total cost of producing q units is given by the* cost function*
_{};

b) the
revenue from selling q units is given by the *revenue function*
_{};

c) the
profit from producing and selling q units is given by the *profit
function* _{}

d) the
break even point is determined by solving the equation

_{}

This
is also illustrated in the figure below.

e) The
average cost is _{.}

#### Example 2

Sometimes
the average variable cost is not constant. Suppliers might
give a discount for large orders, which would make the average variable
cost decrease as output increases. For example, if the average
variable cost is _{}, then this decreases as _{} increases. Assume again that
the fixed costs are still $100 and that the selling price is $2.50
per unit

a) The
cost function is _{}.

b) The
revenue function is _{}.

c) The
profit function is

_{}

d) The
break even point is determined by solving the quadratic equation

_{}

_{}

We
select the positive answer. Note that _{}. See the figure below for a graphical solution.

e) The
average cost is _{}

#### Example 3

On
the other hand, increased production might create a shortage of
raw materials and so drive up the production costs. In this
case, the average variable cost will increase. For example,
if the average variable cost is _{} while the fixed costs are
still $100 and the selling price $2.50 then

a) the
cost function is _{};

b) the
revenue function is _{};

c) the
profit function is

_{}

d) the
break even point is determined by solving the quadratic equation

_{}

_{}

This
has no real solution, and there is no break even point. The
graph below is informative. Notice that at a selling price
of $2.50, selling more and more products leads to an increase in
your loss.

e) _{}

#### Example 4

Assume that the fixed
cost is $1000 and the average variable cost of producing q units
is _{}. What should you set as the selling
price if you want to break even when output is 800 units?

First, determine the
cost function. _{}. The cost of producing 800 units is _{} and the average cost per unit is _{}. Therefore the selling price should be $533.25.
The revenue function will be _{} and cost = revenue when q = 800.

### Marginal Quantities

The
*marginal cost* is the change in total cost which results
from producing one additional unit. When the output is q,
the marginal cost is

_{};

this
is the slope of the line between the points _{} and _{}. The derivative _{},which is the slope of the tangent
line at, gives a good approximation to the exact change in cost,
and it is customary to use the derivative to compute the marginal
cost.

The
*marginal revenue* is the additional revenue derived
from the sale of one additional unit,

_{}.

As
with the cost function we will use the derivative of the revenue
function to determine marginal revenue.

The *marginal profit* is the additional profit derived from
the sale of one additional unit,

_{}.

Again,
we will use the derivative of the profit function to determine marginal
profit. Note that this is the difference between marginal
revenue and marginal cost,

Marginal Profit = Marginal Revenue - Marginal Cost.

**Important
Observation - If the profit function has a maximum, this occurs
when marginal revenue = marginal cost.**

We return to the examples.
For each, we determine marginal cost, revenue and profit; also,
we determine when profit is maximum.

#### Example 5

If the fixed costs are
$100 if the average variable cost is $2, and if the selling price
is $2.50 per unit then we determined the* *cost function is
_{}, the revenue from selling q units is revenue
function _{}, and the profit function is _{}.

a) The
marginal cost is _{}. Notice in this case that this is
exactly the same as the quantity _{}and this is the same as the average variable cost
per unit.

b) The
marginal revenue is _{}. Again, notice in this case that
this is exactly the same as the quantity _{} and this is the selling price per unit.

c) The
marginal revenue is_{}, and this is the profit per unit.

d) The
profit function is increasing and so the profit function has no
maximum.

#### Example 6

If
the average variable cost is _{}, the fixed costs are $100 and that the selling
price is $2.50 per unit. Then the cost function is _{}, the revenue function is _{},
and the profit function is _{}

a) Compute
the marginal cost using the derivative. Thus, _{}. The _{}marginal cost decreases as the output increases.
This makes sense since the average variable cost is decreasing.

i)
For example, if the quantity produced is 60 units, the actual
cost of producing an additional unit is _{} while the marginal cost, computed using
the derivative, gives _{}. See the figure below.

ii) If
the quantity produce is 80 units then the actual cost of producing
an additional unit is _{} while the marginal cost, computed
using the derivative, gives _{}. See the figure below.

b) The
marginal revenue is the same as in the previous example, _{}.

c) The
marginal profit is _{}.

d) Since
_{}, the profit functions is always increasing an there
is no maximum profit.

#### Example 7

In
this example, the average variable cost is _{}, the fixed costs are $100 and the selling
price is $2.50. Then the cost function is _{}, the revenue function is _{}and the profit function is _{}.

a) The
marginal cost is _{}.

b) The
marginal revenue is the same as previously, _{}.

c) The
marginal profit is _{}

d) The
profit is maximum when _{} (notice that _{} and so this critical value will produce a
maximum). Solving

_{}

Therefore
profit is maximum when the output is 25. The maximum profit
is _{}-93.75. In other words, you are still losing
money (profit is negative) but this is the least you would use.

### Supply and Demand

A
*supply curve* describes the relationship between the
quantity supplied and the selling price. The amount of a good
or service that producers plan to sell at a given price during a
given period is called the *quantity supplied*. The quantity
supplied is the maximum amount that producers are willing to supply
at a given price. Quantity supplied is expressed as an amount
per unit of time. For example, if a producer plans to sell
750 units per day at $15 per unit we say that the quantity supplied
is 750 unit per day at price $15.

Similarly, the amount of a good or service that consumers plan to
buy at a given price during a given period is called the *quantity
demanded*. The quantity demanded is the maximum amount
that consumers can be expected to buy at a given price, and it also
is expressed as amount per unit of time.

The *equilibrium price* is the price at which the quantity
demanded equals the quantity supplied. The *equilibrium
quantity*. is the quantity bought and sold at the equilibrium
price. If the curves are graphed on the same coordinate system,
the point of intersection is the* equilibrium point*, and is
where supply equals demand. If the price is below equilibrium
there will be a shortage and the price will rise, while if the price
is above equilibrium there will be a surplus and the price will
fall. If the price is at equilibrium it will stay there unless
other factors enter to cause changes.

#### Example 8

Assume that the supply
function is _{} and the demand function is _{}. The breakeven point is found by setting
equating the two functions and then solving the resulting equation:

_{}

This gives the first
coordinate; the second coordinate is _{} (or, using the demand equation, _{})

#### Example 9

We make the following
assumptions about supply and demand.

- The supplier will
produce 1000 units when the selling price is $20 per unit and
will produce 1500 units if the price is $25 per unit.
- Consumers will demand
1500 units when the selling price is $20 per unit but that the
demand will decrease by 10% if the price increases by 5%.
- Both supply and demand
functions are linear.

Determine the supply
function, the demand function and the equilibrium point.

1)
To determine the supply function, we use a _{} coordinate system and write the equation of
the line through the points (1000,20) and (1500,25).

_{}

2)
For the demand function, one point is (1500,20). If
the price increases 5% to $21, the demand will decrease 10% to 1350.
Thus the second point is (1350,21) and we can now determine the
demand function. _{}