Cost: C = fixed cost + variable cost (C= 270 +
.15x)
Price Demand: p(x) = 300 – .50x
Revenue: R(x) = x[p(x)] => (x)( 300 – .50x) = 300x
– .50x2
Profit: P = Revenue (R) – Cost (C)
Price-Demand (p): is usually given as some P(x) =
–ax + b
However, sometimes you have to create P(x) from price information.
• P(x) can be calculated using point slope equation given :
Price is $14 for 200 units sold. A decrease in price to $12 increases units sold
to 300.
p(x) = m(x – x1) + p1 substitute the calculated m and
one of the units (x1) and price (p1)
p(x) = –.02(x – 200) + $14 = – .02x + 4 + 14 = − .02x + 18
Break Even Point:
R(x) = C(x)
| Where P(x) and R(x) cross. In this case there are
two intersect points. Generally we are only interested in the first one
where we initially break even. |
Average Cost 
is
the cost per unit item
Average Price 
is the price per unit item
Marginal (Maximum) Revenue:
solve for x at R’(x) = 0
Marginal Cost: 
solve for x at C’(x) = 0
Marginal Profit: 
solve
for x at P’(x) = 0
Marginal Average Cost:
Elasticity: 
Demand as a function of price: x = f (p)
E(p) = 1 unit elasticity (demand change equal to price
change)
E(p) > 1 elastic (large demand change with price)
E(p) < 1 inelastic (demand not sensitive to price change)
x = f(p) = 10000 – 25p2
Find domain of p:
Find where E(p) is 1:
(remember there is no negative value for p)
Relative Rate of Change (RRC)
(find the derivative
of f(x) and divide by f (x))
Also can be found with the dx( ln (f(p))
Demand RRC = dp [ ln (f(p)) ]
Price RRC = f(x) = 10x+500
( log expansion )
( ln10 is a constant so dx ln(10) = 0 )
Future Value of a continuous income stream:
Continuous income f low 
Future value: 12%
Tim: 5 yrs
FV = $3754
Surplus:
PS (producer’s surplus) =
CS (con sumer ’s surplus) =
Equilibrium is when: PS = CS
is the current supply
is the current price
The surplus is the area between the curve 
and
the area of the box created by the equilibrium point (
). In Case A it is the (area of the box) – (
the area under the curve); in Case B it is the (area under the curve) – ( area
of the box).
