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- microeconomics formulas and graphs pdf
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microeconomics formulas and graphs pdf
It is said that a picture is worth a thousand words. Likewise, a graph can often be used to better understand relationships between variables. Recall that on a graph, there is a horizontal axis and a vertical axis.
Along the horizontal axis, we start at the origin or a zero. To the right numbers increase and to the left numbers decrease. On the vertical axis, we also start at the origin or zero and the numbers as we go up increase and the numbers as we go down decrease. Combining the horizontal and vertical axes allow us to look at the relationships between variables in two-dimensional space. While we will at times use all four quadrants, we typically spend most of our time in the first quadrant or the space where both the horizontal and vertical variables are positive.
In our example, there is a linear relationship between x and y. We can express the same information, using an equation. The intercept value is the value of y when x is zero. In modeling causal relationships, the value of an endogenous or dependent variable depends upon the value of other variables in the model. When graphing, we typically place the dependent variable on the vertical or y-axis. Those variables whose values are determined outside the model are known as exogenous or independent variables.
These are typically graphed on the x or horizontal axis. A positive or direct relationship between the two variables occurs when the increase in the independent variable causes an increase in the dependent variable. For example, as income increases the amount people will consume also increases. A negative or inverse relationship occurs when the increase in one variable decreases the value of the other variable.
As the price of a good falls, the number of people willing to buy the good increases. In our equation, there is a positive relationship between x and y. When x increases by one, y increases by 2. The slope of a line is determined by taking the change in the vertical amount divided by the change in the horizontal amount. We will let the Greek symbol Delta represent the change. In our example, as x increases by 2, y increases by 4 so the slope would a positive 2. From an equation, we are able to derive the points in a table by plugging in the values of x and computing the value of y.
A curve will have different slopes at different points along the curve. By taking the change in y over the change in x, we are able to get an estimate of the curve at that point. As shown in the table, the slope gets steeper as we move along the curve.
If we compute the slope over a distance around three, we find that the slope from 0 to 6 is 12 and from 2 to 4 is also In doing so, we would find the slope is again As economist look at relationships between variables, they want to know what will be the change in one variable given a change in another variable.
As the change in x gets smaller and smaller, we find the get the slope of the tangent. Thus, being able to compute the slope of the tangent tells us what the marginal change is in the dependent variable. One powerful mathematical tool in calculus is called the derivative. The derivative tells us the slope of the curve at a particular point.
Although it is not a requirement for this class, an example is provided for those who have previously had calculus. The derivative simply tells us the change in y given a very small change in x, or in other words the slope of the curve at a particular point. Increases in the intercept value shifts the curve upwards by the amount of the increase in the intercept. In our example, the intercept value is increased from 2 to 4. Often, we want to find an equilibrium where the one curve would intersect with another, such as with supply and demand.
We are able to find the market equilibrium either by graphing or algebraically. We could simply plug in values, plot the points, and find where demand intersects supply. If we graph it, we find that at price of 30 dollars, the quantity supplied would be 10 and the quantity demanded would be An alternative way, is to solve the problem algebraically. Since at equilibrium the quantity supplied equals the quantity demanded and the price will be the same for both.
We are able to set the two equations equal and solve. Our first step is to get the Qs together, by adding 2Q to both sides. On the left hand side, the negative 2Q plus 2Q cancel each other out, and on the right side 2 Q plus 2Q gives us 4Q. Our next step is to get the Q by itself. The last step is to divide both sides by 4, which leaves us with an equilibrium Quantity of Math as a tool enables economists to determine the optimums. For example, where profits are maximized or costs are minimized.
Finding the slope of a curve can be extremely useful when determining the maximum or minimum. If the company wants to find how many workers will maximize their output, they would look at the point where the slope of the curve goes to zero. In our example if the company wanted to maximize output, it would use 8 workers to do so. Charts and graphs are frequently used to display information. A pie chart shows the portion or relative magnitude of the total amount that is made up by each of the components.
For example, these pie charts display the sources of federal government revenues and the main areas of federal government expenditures. A bar chart shows the amount or magnitude of each item by the length of the item. In this bar chart the number of business as sole proprietorships, partnerships, and corporations are shown on the left while the respective amounts of revenue that each generates annual is shown on by the bar on the right.
Data: Statistical Abstract of the U. A time series displays the data values over time. Time is along the horizontal axis and the observations are evenly spaced, such as annually, quarterly, or monthly.
This graph shows the receipts and outlays of the federal government using the vertical axis on the left hand side or primary axis, and the budget surplus which uses the vertical axis on the right hand side or secondary axis.
Cross sectional data looks at various segments of a population at a point in time. This table displays the median weekly earnings and the unemployment rate in based on the level of education. As seen from the data, those with more education tend to have greater earnings and lower unemployment rates.
Panel data combines cross sectional information and time series. This graph displays the unemployment rate by race over time. From this graph, we can see how the unemployment rate varies by race in any given year, as well as how these rates change over time.
Another useful tool in economics is the growth rate. A growth rate measures the percentage change in a variable and is calculated by taking the difference between the new value and the old value then dividing the change by the old value.
When multiplied by , the rate becomes a percentage. Another important concept in economics is that of average and marginal amounts. The marginal revenue is the additional revenue per car.
The marginal revenue is computed by taking the change in total revenue divided by the change in the number of cars. The average tax rate would be the total tax amount paid divided by the taxable income. Another important concept is to determine the area of a triangle. The area is computed by multiplying one-half times the base times the height. In our example the height is 6 and the length is 10, so the area would be The purpose of math is to help simplify the complex realities of the world.
Hopefully, by completing this math review you will find it easier to interpret some of the graphs and charts that you will see throughout this course. If you want a more detailed math review, you may wish to review Chapter 21 of the Rittenburg and Tregarthen text available at the web page below.
Plotting Points on a Graph If the various values of x and y are given, the points can be plotted on the graph. Once the points are plotted, the dots can be connected to form a line or curve.
Slope of a Curve A curve will have different slopes at different points along the curve. The derivative gives us the slope of the curve. Increases decreases in the slope causes the curve to be steeper flatter. Equilibrium Often, we want to find an equilibrium where the one curve would intersect with another, such as with supply and demand.
Solving Algebraically An alternative way, is to solve the problem algebraically. Charts and Graphs Charts and graphs are frequently used to display information.
We now turn our attention to the demand and supply of resources also called inputs or factors. Resources are used in the production of goods and services. The demand for an input or resource is derived from the demand for the good or service that uses the resource. Consumers do not directly value steel, in and of itself, but since we demand cars, we indirectly demand steel. If the demand for cars increases, there would be an increase in the demand for the steel that is used to make cars. Understanding derived demand and the supply of inputs can help us understand how the markets for inputs function, and in turn, how these markets relate to the markets for final goods i. These answers depend on the value or revenue generated by using an additional amount of the input in question i.
Using Graphs and Formulas Elements of Macroeconomics Johns Hopkins Acces PDF Microeconomic Formulas Cheat Sheet 9 Key Microeconomics Formulas.
ap microeconomics cheat sheet pdf
Here is a list of some of basic microeconomics formulas pertaining to revenues and costs of a firm. The gross domestic product can be expressed as per the expenditure approach and the net income approach. Title: Microsoft Word - Graphs and Models review.
It is said that a picture is worth a thousand words. Likewise, a graph can often be used to better understand relationships between variables. Recall that on a graph, there is a horizontal axis and a vertical axis. Along the horizontal axis, we start at the origin or a zero. To the right numbers increase and to the left numbers decrease.
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