Economics using calculus will allow us to utilize theoretical concepts, in order to calculate real life, and practical problems. These problems include, finding the elasticity of demand curves, as well as, minimizing cost, finding max profitability as well as max revenues when looking at production functions.
Calculating Elasticity
The price elasticity, shows how there is a change in demand, or supply in relation to a change in price.
The following steps will help determine the Price Elasticity
1. There are two things needed in order to calculate a price elasticity. First, the slope of the curve is needed, and secondly, a price point and quantity point, at the desired elasticity point is needed .
1a. When calculating the demand between two specific points, make sure to use an average between the prices and quantities provided.
2. If the quantity or the price is not given within the question, use one or the other, in conjunction with the equation for the curve, to find both variables needed.
3. Lastly arrange the variables in this fashion in order to achieve the elasticity of the curve.
d
Q
d
P
∗
P
Q
{\displaystyle {\frac {dQ}{dP}}*{\frac {P}{Q}}}
'or'
d
Q
d
P
∗
P
∗
Q
∗
{\displaystyle {\frac {dQ}{dP}}*{\frac {P*}{Q*}}}
, where P* and Q* represents averages between two prices and two quantities.
Videos
Price Elasticity of Demand
Price Elasticity of Supply
Minimizing Average Cost
Steps to Minimizing Average Cost are:
1. Take the derivative of the cost equation to find the marginal cost for each project.
2. Then divide by the variable in order to find average cost per unit.
3. Equate the marginal cost function and the average cost function and solve for x.
Maximizing Revenue / Profits
The first part of this video will show how to create maximum revenue while the second part will show how to create maximum profit.
Steps to Maximizing Revenue
1. Realize that revenue is the price per unit times the amount of units sold.
2. Use the information from the question to set up the revenue function
3. Take the derivative of the revenue function and find solve for 0 as R'. This will give you critical points.
4. One of the critical points will be the the generator from maximum revenue. Use the second derivative test to check, and also make sure that it is in the constraints of the prive range. (the video will explain more)
Steps to Maximizing Profit
1. Realize that profit is the revenue minus the cost.
2. Set up and equation using the given information. Remember revenue is the amount of units sold multiplied by their price. The cost function is usually given to you.
3. Take the derivative of the profit function and solve for P' = 0.
4. Determine the critical points and use the second derivative test to determine the correct value. Also make sure the answer is within the bounds of the price or quantity. (video will explain more)
Very Important
!!!!Always make sure to read the question carefully and answer the question as it states. Do not answer more or less than is requested!!!!
