Download 1st five terms

Math 220 - Calculus for Business and Management - Economic Terms
Price – The amount charged per item for products sold.
Quantity – The number of items produced or sold. For our purposes the number produced will be equal to
the number sold. This is frequently a function of the price. In general, raising the price reduces the number
of items that can be sold (See Elasticity).
Revenue – The total amount of money taken in from the sale of products. Revenue is the quantity sold times
the price for each item (Quantity times Price)
Cost – The cost to produce all the items. This is usually made up of fixed costs (like rent) that donŠt change
no matter how many items are produced and variable costs that depend on the number of items produced.
Profit – The amount of money left over after all the bills are paid. (Revenue - Cost)
Elasticity – A measure of the response of the marketplace to the price. If elasticity is less than 1, the demand
is inelastic. That means that the quantity sold will stay about the same even though the price is increasing. If
elasticity is greater than 1, the demand is elastic. That means that the quantity sold will go down as the price
goes up. When the elasticity equals zero, the revenue is the highest it can be.
If p represents price and q represents quantity sold (where quantity is a function of the price) the equation for
elasticity is
E(p) = −
p dq
q dp
Marginal Revenue, Cost, Profit – Marginal values are the rate at which the revenue, cost or profits are
changing as a function of the price. They are found by taking the derivative of the revenue, cost and profit
functions. These are useful in finding the maximum revenue and profit or the minimum cost.
Numerical Example
Price: $5.00/ item
Quantity: 200 items
Revenue: 200 × $5.00 = $1000
Cost: $400 fixed costs, $2 per item: $400 + $2 × 200 = $800
Profit: $1000 − $800 = $200
Examples Using Functions
Price: Let p represent the price
Quantity: q(p) = 225 − p2 . This means that 224 items can be sold for $1.00. If the price is $2.00, only 221
items are sold. If the price is $3.00, 216 items are sold etc.
Revenue: (225 − p2 ) · p = 225p − p3
Cost: C(q) = 300 + 2q. This means that there is a fixed cost of $300 and a variable cost that is $2 per item
sold. Since q is the quantity, the q in the equation for cost can be replaced with the quantity function. Cost
can then be written another way (as a function of price):
C(p) = 300 + 2(225 − p2 ) = 750 − 2p2
1
Profit:
225p − p3 − (750 − 2p2 ) = 750 + 225p + 2p2 − p3
Elasticity:
E(p) = −
p
− 2p2
(−2p) =
q
225 − p2
Elasticity = 1 when
2p2
=1
225 − p3
2p2 = 225 − p2
3p2 = 225
s
√
225
p =
= 5 3
3
Since the square root of 3 is approximately equal to 1.73, when the price is less than about $8.65, the demand
(quantity sold) will not change very much and revenue will continue to rise. When the price goes above
$8.65, the demand will drop and revenue will start to fall. Therefore $8.65 will give the greatest revenue for
this product.
2