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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). Integration. Big Ideas What is an antiderivative , how do we determine one, and how do we represent it with symbols?

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

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  1. Applied Calculus (MAT 121)Dr. Day, Monday, April 2, 2012 • Area Between Curves (6.6) • Revisit Supply & Demand: Consumer and Producer Surplus (6.7) MAT 121

  2. Integration Big 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. MAT 121

  3. 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). MAT 121

  4. Area Between Curves MAT 121

  5. Area Between Curves Determine the area trapped between the curves y = √xand y = x − 2, bounded on the left by the y-axis. MAT 121

  6. 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

  7. Revisiting Supply & Demand Calculate the equilibrium priceand the quantity supplied/demanded at that price. MAT 121

  8. 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

  9. 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 121

  10. MAT 121

  11. Using Calculus to Determine Surplus MAT 121

  12. Assignments WebAssign 6.4 due tonight 6.6 due Wednesday night 6.7 due Thursday night Test #5 (Chapter 6): Friday, April 6, 2012. MAT 121

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