During my first year in university, I had a roommate who was majoring in economics. Among some of her reasons for choosing this course of study\u00a0was the simplicity of the mathematics included -- or so she thought. The following weeks of lectures gave her a nasty shock. Mathematics is a crucial and vital part of economics.<\/p>\n
Algebra is a set of mathematical expressions containing variables, constants, and operations. Before you\u00a0can fully understand economics, you need a good understanding of these mathematical concepts. Calculating profits, returns, allocation of resources, investment risks, among other things, require you to know\u00a0how to identify and calculate variables, and constants. Most economic\u00a0calculations and measurements contain statistics, algebra, and calculus (differential equations).<\/p>\n
Economists assess\u00a0risks involved with a particular event and find ways to save money using math. Big companies hire\u00a0economists to determine which course of action is best for their business. The economist conducts a market survey and notes down all the factors in play. These factors, also known as constants and variables, are used to calculate particular outcomes that determine if an\u00a0action will be profitable or not and what the long-term\u00a0ramifications may be.<\/p>\n
There are three fundamental laws of algebra: commutative, associative, and distributive.<\/p>\n
The\u00a0commutative law<\/strong>\u00a0states that addition or multiplication of two or more numbers is commutative. The order at which they are placed doesn\u2019t matter, i.e. 2+3+4=4+2+3 and 1x2x3=3x2x1<\/p>\n The\u00a0associative law<\/strong>\u00a0states that the grouping of numbers doesn\u2019t affect the result when adding or subtracting them, i.e. 1+2 + (3+4) = 1+ (2+3) +4 and 2(3x4) = (2x3) x4.<\/p>\n The\u00a0distributive law<\/strong>\u00a0states that (X+Y) Z=XZ + YZ and X(Y+Z) =XY+XZ, which means multiplying a number separately or as a group yields the same result.<\/p>\n We will use these laws to solve some friendly economic problems that contain algebraic equations.<\/p>\n We will first present the questions. A\u00a0break down of each question is included in the section below.<\/p>\n A cosmetic company just started a new face cream product line. The company produces 800 face creams in a week. The company offers \"pay on delivery\" services. For each customer that orders the face cream, there is a 10%\u00a0chance that they may cancel the order before the week runs out. This means that there is a 90% chance they won\u2019t. If the company receives 800 orders for the week, how many people are expected to cancel their orders?<\/p>\n A coffee shop has about 10,000 USD worth of assets before depreciation. After assessing the shop, you realize that the cost of repair will be four times the cost of maintenance. The expected repairs and maintenance expense to fixed assets ratio is given at 8% using this formula:<\/p>\n Repairs and Maintenance Expense to Fixed Assets Ratio = (Cost of Repairs + Cost of Maintenance) \/ Total Value of Fixed Assets.<\/em><\/p>\n Determine how much money will be needed to put the shop back in working order and if it is worth\u00a010,000 USD.<\/p>\n A company is starting on new product X\u00a0but has\u00a0yet to determine the price of the product. They aim to price the product such that their demand will be the same as the number of products manufactured. X is bought based on how much it costs, and a study shows that the\u00a0demand per month is three times the price subtracted from 21. The quantity that can be manufactured is 4 times the price plus 3. What will be the expected product price?<\/p>\n Let us assume that you are a financial analyst with the following data, and you want to find the return on assets for a company to see if it\u2019s making enough money.<\/p>\n Financial Leverage Index = 3 and the Return on Equity (ROE) is 50% of the total capital. What is the Return on Assets (ROA)?<\/p>\n When someone orders a face cream, they either cancel the delivery or do not. Let\u2019s say that\u00a0X<\/em>\u00a0is the number of people that do not cancel their orders. This means that\u00a0X<\/em>\u00a0is binomially distributed.\u00a0P<\/em>\u00a0is the probability of not canceling, and\u00a0n<\/em>\u00a0is the quantity ordered. The probability distribution is:<\/p>\n P(x;n,p)=(nx)px(1\u2212p)n\u2212x,\u00a0x=0, 1,...n<\/em><\/p>\n The mean of the distribution is\u00a0E(x) = np<\/em>\u00a0and the variance\u00a0\u03c32 = np(1\u2212p)<\/em>.<\/p>\n In this problem n=800 and p=0.9.<\/p>\n E(x) = 800 x 0.9 and \u03c32 = 800 x 0.9 (1\u22120.9)<\/em><\/p>\n So, E(X) = 720 and \u03c3 = 8.49 and the expected cancels is 80.<\/p>\n Since Quantity demanded = Quantity supplied, we can say that\u00a021\u22123P = 3+4P<\/em>.<\/p>\n Subtracting 3 from both sides and adding 3P to both sides yields:<\/p>\n 21\u22123P\u22123\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3+4P\u22123<\/em><\/p>\n 21\u22123P\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a04P<\/em><\/p>\n 21\u22123P+3P\u00a0\u00a0\u00a0\u00a0\u00a0\u00a04P+3P<\/em><\/p>\n 21\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a07P<\/em><\/p>\n Divide both sides by 7.<\/p>\n 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 P<\/em><\/p>\n This means that for the company to be able to supply what is demanded, they need the price to be at $3\u00a0per product.<\/p>\n The total amount of money required will be the sum of the cost of repairs and the cost of maintenance. Let's assume that the cost of maintenance is\u00a0m<\/em>. This means that the cost of repairs is\u00a04m<\/em>.<\/p>\n 0.8 = (m + 4m) \/10,000<\/em><\/p>\n M+4m = 10,000 x 0.8<\/em><\/p>\n 5m = 8000<\/em><\/p>\n M = 8000\\5<\/em><\/p>\n M = 1,600 and most of repairs is\u00a03 x 1600<\/em>=6400<\/p>\n This means the cost of the coffee house is almost the same as how much it will take to renovate it.<\/p>\n Let\u2019s break down the problem to identify the meaning and value of the different variables.<\/p>\n The formula for the financial leverage index is:<\/p>\n Financial Leverage Index = Return on Equity (ROE) \/ Return on Assets (ROA)<\/em><\/p>\n Let's assume that\u00a0ROA = x<\/em>.<\/p>\n 3 = 56% \/ X<\/em><\/p>\n 3*X =56%<\/em><\/p>\n X= 56\/3<\/em><\/p>\nQuestions<\/h2>\n
Question One<\/h3>\n
Question Two<\/h3>\n
Question Three<\/h3>\n
Question Four<\/h3>\n
Solutions<\/h2>\n
Solution One<\/h3>\n
Solution Two<\/h3>\n
Solution Three<\/h3>\n
Solution Four<\/h3>\n