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Determine the (a) consumers surplus and (b) producers surplus for the given demand and supply curves..$$2 p+x-300=0,8 p-x-200=0$$

(a) 10,000(b) 2500

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 8

Applications of the Definite Integral

Integrals

Campbell University

Oregon State University

Baylor University

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

03:06

Find the consumer and prod…

01:38

05:13

Consumer Surplus and Produ…

01:48

Find the consumers' s…

this problem we are asked to find the consumer and producer surpluses for a demand function of 300 minus X. They supply function of 100 plus X. So the first thing that we're going to need to do is solve for the X value where we have equilibrium between supply and demand. So we said, we'll see daisy, we said supply 300- X equal to demand or opposite way around, but no difference here significantly. Uh So we can add X to both sides, subtract 100 from both sides, so we'll get to X equals 200 therefore X is going to equal 100. Then we can plug that back into one of our price functions and figure out that the price at 100 The equilibrium price is going to be 200. So now that we have that the consumer surplus, which I'll call sc going to be the integral from zero up to 100 of the demand function minus the price. That's 300 minus x minus 200. Which will be just 100 minus X. D X. So that will be 100 X minus X squared over two, Evaluated from zero up to 100. So that will be uh one second here Will be 100,000 or sorry, 10,000 rather 10,000 -10000 over two. So 10,000 -5000. So the result there should be 5000 and then the producer surplus Is going to be the integral from 0 to 100 Of the price. 100 minus the supply function. There will be 100 minus one. Yeah. Excuse me. One second here. All right. So yeah, that will turn out to be 100 -100 -1. So that will be just negative x dx evaluated from 0 to 100. So that will turn out to be negative X squared over two I evaluated from 0 to 100. So the result there Is going to be negative 5000. Excuse me, That should be 200 minus X. So 200 X. So 20,000 minus 5000. So the result there should be 15,000, I believe. One second. Yeah, no, I take that back. It was only in the producer surplus that I screwed that up. So the actually this should be down here 200 minus X. So that's going to it would be 200 minus 100 minus x. So that will turn out to be 100 minus X there. So the result that we arrive at, when we actually do everything properly here should be the same thing as what we had above. Essentially we should end up having At the end of the day we should end up having 5000 for the producer surplus

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