Mathematical Economics Tutor London
Work with our PhD Mathematical Economics Tutor in London. for Maths for Economics I & II. Our tutors cover math for economics, mathematical finance, quantitative economics and econometrics.
Eqonomica’s GPD grew by 6% in 2016. Suppose it will keep growing continuously at the same rate for the next 5 years. What will the cumulative percentage growth over these 5 years be?
You know you’ll have $100 in a year. How much can you borrow at 10% interest if it is added continuously?
Consider a function y = f (x). Suppose we are interested in measuring the area A under that function and between two values of x: a and b.
We can approximate the area by a rectangle. Or several of them. The more we use, the smaller the error. If we keep adding more and more rectangles: When the number of rectangles becomes infinitely large, the sum of their areas approaches the shaded area A. In trying to solve the area problem we have to ask ourselves: What is the meaning of the word area? This question is easy to answer for regions with straight sides. For a rectangle, the area is defined as the product of the length and the width. The area of a triangle is half the base times the height.
Recall that in defining a tangent we first approximated the slope of the tangent line by slopes of secant lines and then we took the limit of these approximations. We pursue a similar idea for areas. We first approximate the region by rectangles and then we take the limit of the areas of these rectangles as we increase the number of rectangles.
dx is an infinitely small change in x. A and b are the limits of integration. The expression reads: “A is the denite integral of the function f (x) between the limits a and b”
First Fundamental Theorem of Calculus
Imagine you are driving a car but the odometer is broken. Therefore, you have no idea how far you’ve travelled. However your speedometer works and you have a stopwatch.
You can check the speed and measure an interval of time. Multiplying the two will tell you how far you travelled in that interval of time.
Now imagine doing it time after time, so that at any point in time you know how far you travelled during the previous interval. It’s an approximation of the total distance you’ve covered. However, it’s hard to maintain a constant speed. For the approximation to be any good you need to make the time intervals very small. If you make them infinitely small you’ll know the exact distance.
The total distance is the integral of your speed. At the same time, speed is the first derivative of covered distance. It tells you how the distance changes.
Economics Application: Consumer Surplus
Consumer surplus is the area below the demand curve and above market price. If the demand curve is non-linear, as is the case in reality, then consumer surplus is not straightforward to calculate. Instead of being a triangle, it becomes an area under the curve which must be found using integration instead of simple formulas of triangle or trapezoid. Our math for economics tutor will explain applications of all calculus concepts to economics so students are able to build and link these concepts.
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