Conceptual Understanding
At what quantity of donuts is the profit of the donut shop maximized?
When marginal profit=0, when mr=mc.
If a company sells donuts at 5 dollars per donut, what is the marginal revenue from one donut?
5 dollars
The price per unit is given as P(x)=2000-x and the cost function is given as C(x)=100+4x, what price should be charged to maximize profit?
R(x)=x(2000-x)
The profit function is R(x)-C(x)
= 2000x-x2-(100+4x)=2000x-x2-100-4x
=1996x-x2-100
Therefore, the marginal profit function is:
Mp(x)=1996-2x
x=998
P(x)=2000-x=2000-998
P=1002
Why is there an inverse relationship between price and quantity demanded?
Because of the income and substitution effects. (We CAN buy more and the trade-off between donuts and other goods decreases.)
If the profit and cost functions of a company are
P(x)=3x2-6x+7
C(x)=-3x2+9x-7
What is the marginal revenue function?
R(x)=P(x)+C(x)
R(x)=3x
R'(x)=3
The marginal revenue is 3 dollars per unit.
A company has a revenue function of
R=25x2
as well as a cost function of
C=2x3-50x2+60x+2
At what quantity is the profit maximized?
At x=5.