applied calculus (mat 121) dr. day, monday, april 2, 2012

Applied Calculus (MAT 121)Dr. Day, Monday, April 2, 2012

Area Between Curves (6.6) Revisit Supply & Demand: Consumer and Producer Surplus (6.7)

Monday, April 2, 2012 MAT 121

MAT 121

IntegrationBig Ideas What is an antiderivative, how do we determine one,

and how do we represent it with symbols? How can we determine the area under a curve or

trapped between two curves, and how does the integral relate to that?

The definite integral of a rate function gives use an accumulation.

The Fundamental Theorem of Calculus: Connecting derivatives and integrals.

Monday, April 2, 2012

MAT 121

The Fundamental Theorem of Calculus

Let f be continuous on [a, b]. Then,

where F is any antiderivative of f; that is, F

′(x) = f(x).Monday, April 2, 2012

MAT 121

Area Between Curves


MAT 121

Area Between Curves


Determine the area trapped between the curves y = √x

and y = x − 2, bounded on the left by the y-axis.

MAT 121

Area Between Curves


Determine the area trapped between the curves y = 4 – x2 and y = 2x + 1, bounded on the left by the line x = −1 and on the right by the line x = 1.

MAT 121

Revisiting Supply & Demand


Calculate the equilibrium price and the quantity supplied/demanded at that price.

MAT 121

Supply and Demand:

Determining Surplus


The concept of consumer’s surplus was introduced by Alfred Marshall:

"A consumer is generally willing to pay more for a given quantity of good than what he actually pays at the price prevailing in the market".

For example, you go to the market for the purchase of a pen. You are mentally prepared to pay $25 for the pen which the seller has shown to you. He offers the pen for $10 only. You immediately purchase the pen and say ‘thank you’.

You were willing to pay $25 for the pen but you are delighted to get it for $10 only. Consumer’s surplus is the difference between the maximum amount a consumer is willing to pay for the good and the price he actually pays for the good. In our example given above, the consumer’s surplus is $15 ($25 – $10).

MAT 121

Supply and Demand:

Determining Surplus


Producer Surplus: An economic measure of the difference between the amount that a producer of a good receives and the minimum amount that he or she would be willing to accept for the good. The difference, or surplus amount, is the benefit that the producer receives for selling the good in the market. For example, say a producer is willing to sell 500 widgets at $5 a piece and consumers are willing to purchase these widgets for $8 per widget. If the producer sells all of the widgets to consumers for $8, it will receive $4,000. To calculate the producer surplus, you subtract the amount the producer received by the amount it was willing to accept, (in this case $2,500), and you find a producer surplus of $1,500 ($4,000 - $2,500).

MAT 121Monday, April 2, 2012

MAT 121

Using Calculus to Determine

Surplus


MAT 121

WebAssign6.4 due tonight6.6 due Wednesday night6.7 due Thursday night

Test #5 (Chapter 6): Friday, April 6, 2012.

Assignments


applied calculus (mat 121) dr. day, monday, april 2, 2012

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