LAVC Calculus Consumer and Producer Surplus Project

Consumer’s and Producer’s Surplus Task #1The purpose of this task is to be able to create a business example where two important business concepts, the consumer’s and producer’s surplus apply.Watch the following math talk video if you haven’t done so already to get an idea.Think about a similar situation where consumer’s and producer’s surplus applies. In your video presentation first explain the meaning of consumer’s and producer’s surplus (using your own words, do not read from a script!) then, give an example of a similar situation (similar to what you saw in the math talk video above, but of course a different example). Please note that in Task 2 you will be asked to use your business example that you are giving in this task, so select your example wisely. You may want to read through Task 1 and Task 2 (look at the provided examples) before you think about your business example you describe here for Task 1.Remember not to read from script, you are teaching your audience about a real life application of consumer’s and producer’s surplus. Acquire the knowledge needed to explain these concepts by studying using the provided learning material then share your knowledge, share what you’ve learned.The purpose of this task is to set up and solve definite integrals to find consumer’s and producer’s surplus and interpret the definite integrals graphically.Before you start recording, take the following steps:Refer to Task 1 business example that you gave.Here you need to come up with some example numbers (figures) to use them as your sample data. Consider the following as you come up with your sample data: 1) As price of the goods decreases, more people can afford the product so the demand increases. This results in the demand function to be a decreasing curve (or line). On the other hand, as the price goes up the producer’s will produce more to make more profit. This results in the supply function to be an increasing curve (or line).See the following student example for sample data: ” Let’s suppose that there is an incremental drop in the price of a new dishwasher. As the price drops, a larger number of consumers are able to afford the new dishwasher. The dropped prices and the number of dishwashers sold are as follows: {$400 (10 dishwashers sold at this price), $470 (6 dishwashers sold at this price), $500 (4 dishwashers sold at this price), $550 (3 dishwashers sold at this price), $600 (only 2 dishwashers sold at this price)}; Now let’s look at a producer that’s producing this dishwasher. The price the producer would be willing to charge along with the number of dishwashers produced are as follows:{$450 (5 dishwashers produced), $460 (6 dishwashers produced), $475 (10 dishwashers produced), $485 (12 dishwashers produced), $500 (15 dishwashers produced)}”Next you need to find ?(?), the demand function, and ?(?), the supply function using your sample data. This requires data fitting to find the best equation that could model your situation. To do so, enter your example numbers into an excel spreadsheet. You will need to do this twice (or using two different set of columns), to find D(x) and next to find S(x). To find D(x) enter the consumer data into two columns (for the student example above, the student will enter {10, 6, 4, 3, 2} in the first column for quantity and {$400, $470, $500, $550, $600} in the second column for price, then based on your scatter plot choose the best fitting curve (add trendline). I suggest you assume a linear model for both the demand curve and the supply curve for simplicity of your calculations. See the tutorial video below in finding the best fitting curve. The tutorial shows a cubic curve fitting, based on your scatter plot you can choose linear or a degree two polynomial.Identify the point of equilibrium (?¯,?¯). This is the point of intersection of demand and supply equations. How do we find the point of intersection of two equations (or the point(s) they have in common)? You can discuss this in the discussion forum.Graph ?(?) and ?(?) on the same coordinate system where x-axis is the quantity and the y-axis is the price. Clearly show the point of equilibrium. Shade and clearly label the areas that represent consumer’s and producer’s surplus.Set up and solve the integrals to compute consumer’s and producer’s surplus.Now you are ready to record:In your video presentation walk us through the steps and the process of finding the equations for consumer’s surplus, ?(?) and producer’s surplus, ?(?).In your video presentation show us how to graph these equations on the same coordinate plane. Teach us about the graphical implication of definite integrals, this means teach the graphical meaning of a definite integral. On your graph shade the area that indicates consumer’s surplus. On your graph shade the area that indicates producer’s surplus. What does a definite integral represent?In your video presentation teach us how to set up each definite integral. (one for consumer’s surplus and one for producer’s surplus) Teach us how to set up the limits of integration.In your video presentation teach us how to evaluate each definite integral step by step.Finally in your video representation tell us what do the results of these definite integrals indicate or say about your product.