Questions for Review with Answers
Chapter 4. The Tools of Economics
I. The Maths Survival Kit
Chapter 4 – Question 1
How much is 3/8 in terms of percent?
* 37.5 percent. (100/8 x 3.)
Chapter 4 – Question 2
What are the differences between time-series graphs, bar charts and pie charts?
* All of them illustrate the size of one magnitude. A time-series graph illustrates the development of one magnitude over several years. A bar chart compares the size of this magnitude with the size of other magnitudes. A pie chart does the same but compares percentages, while bar charts compare absolute figures.
Chapter 4 – Question 3
On which axis are the years indicated in time-series graphs?
* On the x-axis.
Chapter 4 – Question 4
Draw a pie chart for the following data: the unemployed account for 5 percent of the labour force.
* Here is some help with the pie chart: The first step is to convert percentages into degrees. A circle has 360 degrees. Divide the percentage by 100 and then multiply the result by 360. In our question the number of degrees is 18. (5/100 = 0.05. 0.05 x 360 = 18). For the second step you need a protractor to show you how to get the 18-degree portion of the pie correct. You can download a protractor from the Web. But I haven't done it, which is why you find no pie chart here.
Chapter 4 – Question 5
Explain the laws of demand and supply and the essence of equilibrium theory and draw the microeconomic standard graph.
* The law of demand states that quantity demanded rises as prices fall. The law of supply states that quantity supplied rises as prices rise. As the responses of supply and demand to prices are diametrically opposed, they act upon each other to restore equilibrium.
Chapter 4 – Question 6
Describe the relationship between endogenous variables.
* The relationship between endogenous variables is such that a change in the independent variable causes a change in the dependent variable. In the standard graph, price is the independent variable, quantity supplied/demanded the dependent variable.
Chapter 4 – Question 7
Distinguish linear and non-linear curves.
* Linear curves are straight lines. Non-linear curves are real curves.
Chapter 4 – Question 8
The demand curve has a negative slope and represents an inverse relationship. Please explain.
* The curve's slope is negative because, when you calculate the slope, you get a minus sign. The relationship is inverse because variables move in opposite directions. When one variable rises, the other one falls.
Chapter 4 – Question 9
The supply curve has a positive slope and represents a direct relationship. Please explain.
* Its slope is positive because, when you calculate it, you get a positive sign. The relationship is direct because both variables move in the same direction. When one variable rises, the other one rises, too.
Chapter 4 – Question 10
How do you calculate the slope of a linear curve?
* Divide the rise by the run: change on y-axis/change on x-axis.
Chapter 4 – Question 11
And the slope of a non-linear curve?
* Draw a straight line that is tangent to one point on the curve. Like any straight line, the tangent has the same slope everywhere. It is calculated with the help of the above formula: Change on y-axis/change on x-axis. The result is the slope of the non-linear curve at the tangency point.
Chapter 4 – Question 12
What does ceteris paribus stand for?
* It stands for all other things remaining equal. The assumption of ceteris paribus is an attempt to imitate experiments in the natural sciences.
Chapter 4 – Question 13
When do the demand and supply curves shift?
* When all other things do not remain equal, i.e. when exogenous variables - variables other than price and quantity supplied/demanded - have changed.
Chapter 4 – Question 14
What is the difference between mathematical economics and econometrics?
* Mathematical economics expresses economic laws in terms of algebra. Econometrics feeds data into models to make forecasts and to simulate the impact of alternative government policies.
II. Advanced Maths Topic
Chapter 4 – Question 15
Distinguish linear and non-linear equations.
* Linear equations have variables with an exponent of 1; non-linear equations have variables with an exponent of 2 or higher.
Chapter 4 – Question 16
What is the typical characteristic of simultaneous equations?
* They are a set of equations that have at least one common solution. The number of unknowns is matched by the number of equations.
Chapter 4 – Question 17
Distinguish equations and identities.
* Equations have one or several solutions. Sometimes they even have infinitely many solutions (for instance, 2x + 2y = 2). Identities are by definition true for innumerable variables.
Chapter 4 – Question 18
Give two examples of inequalities.
* x ≤ 3, which reads x equal to or smaller than 3.
x ≥ 3, which reads x equal to or greater than 3.
Chapter 4 – Question 19
Write a schedule for the following equation: y = 4x+4.
| * | x | y |
| 1 | 8 | |
| 2 | 12 | |
| 3 | 16 | |
| 4 | 20 | |
| 5 | 24 |
Chapter 4 – Question 20
Draw a curve into a co-ordinate system
A. with infinite slope
B. and another one with zero slope
C. and a third one with positive slope
D. and a last one with negative slope.
Chapter 4 – Question 21
Derive a schedule from the following supply function: Q = P - 3.
| * | P | Q |
| 3 | 0 | |
| 4 | 1 | |
| 5 | 2 | |
| 6 | 3 | |
| 7 | 4 |
Chapter 4 – Question 22
What is a function?
* A function expresses the relationship between variables. It shows how one variable depends on the other. Mathematicians say that a function is a rule by which an input is converted into an output.
III. A Look into Your Mathematical Future
Chapter 4 – Question 23
Why is marginal analysis based on differential calculus?
* Marginal analysis centres around the last unit before reaching a limit after which doing something is no longer worthwhile. The calculus also centres around the notion of limit and allows to calculate maximum - i.e. optimal - values.
Chapter 4 – Question 24
Why is linear programming so suitable to solve economic problems?
* Because it allows to consider constraints, to which economic activities are always subjected. The constraints are due to relative scarcity.
IV. Marginal Analysis
Chapter 4 – Question 25
Explain why, according to marginal analysis, marginal utility equals price.
* Because people buy additional units until marginal utility equals price. Thereafter, price exceeds utility; no further units are bought.
Chapter 4 – Question 26
And why marginal revenue also equals price.
* Because, for the perfect competitor of the micro model, marginal revenue is the price received for the last unit. (For imperfect competitors, this is not the case.)
Chapter 4 – Question 27
And why marginal cost also equals price.
* Because firms expand output until marginal cost equals price.
Chapter 4 – Question 28
Why are mathematical statements about utility impossible?
* Because utility cannot be quantified; there are not utils. Statements about cardinal utility - utility = 3 - are completely impossible. Ordinal statements are possible - the utility of x ranks third - but they do not lend themselves easily to interpersonal comparison.
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