TranscendFinals ENGINEERING ECONOMY. Preface

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1 Preface This booklet contains information from chapters 1 through 8 of McGill s course, FACC 300: Engineering Economy. These chapters are generally tested on the final exam of the semester. This booklet focuses on only the most relevant material of the course with regards to the final exam (i.e. does not include everything in the course); for students wishing to have more information, you can refer to your individual course notes. We at TranscendFinals kindly ask that you do not photocopy, reprint, or post this material. Perpetrators will be tracked down and banned from attending future review sessions. During the review session, the following rules will apply No recordings or flash photography is permitted. Anyone caught doing so will politely be asked to leave. Do not disrupt other attendees during the session. Please do not damage the classroom in any way. We strongly encourage all attendees to provide constructive feedback during the postevaluation to help improve the services of TranscendFinals. i

2 Chapter 1: The Basics of Supply and Demand This chapter is a quick introduction to select economic principles: supply, demand, elasticity, and productivity. 1.1 Supply-demand analysis Supply Curve: A graphical representation of the relationship between the price of a good or service and the quantity supplied for a given period of time. The price is displayed on the y-axis and the quantity supplied on the x-axis. Demand Curve: A graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time. The price is displayed on the y-axis and the quantity demanded on the x-axis. The figure below is a typical representation of these 2 curves. Supply and Demand curve [Ref: investopedia.com] Usually, the demand curve is downward sloping; following the axes, the quantity increases as the price decreases. This makes sense because the demand curve represents how much people want a product. If the product is selling at a lower price than usual, more people will want it. Conversely, the supply curve is upward sloping; following the axes, the quantity increases as the price increases. This makes sense because the supply curve represents how willing a supplier is willing to produce or a product. If the product can be sold at a higher price than usual, suppliers will want to supply more of it. There are different questions or analysis that can be done with just these 2 curves. 1

3 Analysis 1) Equilibrium: The intersection of the supply and demand curves The equilibrium point can be found visually or solved mathematically if the functions of the curves are provided. This intersection is also referred to as the market equilibrium point, and each of the coordinates referred to as the market equilibrium quantity and the market equilibrium price. Question: Find the market equilibrium point of the following demand and supply curves. P Dem = *Q Dem P Sup = Q Sup /12 5 Work Equate the functions to solve for equilibrium points (P Dem = P Sup = P eq and Q Dem = Q Sup = Q eq ) _ 20.1*Q eq = Q eq / = *Q eq Q eq = P eq = * = 6.36 Analysis 2) Shortage/Surplus: Difference in quantities at a certain price If given any price, the difference in the quantity supplied and quantity demanded can be calculated. If the quantity supplied is greater than the quantity demanded, this is a surplus. If the quantity demanded is greater than the quantity supplied, this is a shortage. Shortages occur when the price is lower than the market equilibrium price, and surpluses occur when the price is higher. The figure below shows this behavior. Shortage and Surplus [Ref: oocities.org] The shortage/surplus is the difference in quantities. This may seem a bit awkward to calculate as the quantities are on the x-axis. It is essentially the horizontal distance between the two curves at a given price and usually we take the absolute value and just state if it s a shortage or surplus. 2

4 Question: Find the shortage/surplus of the demand and supply curves at both $5 and $7. P Dem = *Q Dem P Sup = Q Sup /12 5 Work Lock in the prices and solve for the quantities. 5 = *Q Dem Q Dem = = Q Sup /12-5 Q Sup = 120 Demand is greater than supply, therefore a shortage. Difference in values is = $5, Shortage of 30 Lock in the prices and solve for the quantities. 7 = *Q Dem Q Dem = = Q Sup /12-5 Q Sup = 144 Supply is greater than demand, therefore a surplus. Difference in values is = $7, Surplus of 14 Analysis 3) Total Consumer Expenditure: How much was spent at market equilibrium The total consumer expenditure is calculated at the Equilibrium Price x Equilibrium Quantity Analysis 4) Total Consumer Surplus: How much was saved by those willing to buy the product at a higher price Total consumer is the remaining area left under the curve when the total consumer expenditure is removed. The figure below shows this breakdown. Consumer Expenditure and Surplus [Ref: dineshbakshi.com] 3

5 Question: Find the consumer expenditure and surplus of the supply and demand curves. P Dem = *Q Dem P Sup = Q Sup /12 5 Work From our answer in the previous example for the equilibrium, the market equilibrium point is: (136.36, 6.36) The Total Consumer Expenditure is thus *6.36 = Since the demand curve is linear, the consumer surplus area is a triangle. The triangle has a base that is the same length as the market equilibrium quantity (136.36). The height of the triangle is the difference between the y-intercept and the market equilibrium price (6.36). The y-intercept of the demand curve is 20. The total consumer surplus is thus *( )/2 = Analysis 5) Elasticity: The impact of changes that price has on quantity at a specific price and quantity Elasticity is essentially equivalent to a slope calculation that is then multiplied by its coordinates on the curve. The elasticity can be calculated for the demand or the supply curve. For the demand curve, the slope will always be negative, and in this course the elasticities are always reported as positive values, meaning that we will take the absolute value of the elasticity. The slope can either be calculated with a derivative (price elasticity) or between 2 points (arc elasticity). Recall that the curves are displayed with price on the y-axis and quantity on the x- axis, but elasticity is about looking at the effect a change in price has, so the derivate/slope must be taken with quantity as the dependent variable. Question: Find the price elasticity of both curves at the market equilibrium point and compare them to the arc elasticity between prices $5 and $7. P Dem = *Q Dem P Sup = Q Sup /12 5 Work Re-arrange both curves so that Q is the dependent variable. Q Dem = *P Dem Q Sup = *P Sup Price Elasticity at Market Equilibrium E D = - dq dem /dp dem * P eq /Q eq = 10 * 6.36/ = 0.47 E S = dq sup /dp sup * P eq /Q eq = 12 * 6.36/ = 0.56 Arc Elasticity between $5 and $7 Recall the values of quantity at both prices from a previous Q Dem = 150, Q Sup = Q Dem = 130, Q Sup = 144 4

6 E D = -( )/(7 5) * (7 + 5)/( ) = 0.43 E S = ( )/(7 5) * (7 + 5)/( ) = 0.55 The results match up very nicely because of the linear nature of both curves and that the location of the arc elasticity range overlaps with the market equilibrium point. In addition to calculating the elasticity, we can also comment on the values obtained. If the elasticity is greater than 1, it is referred to as elastic (luxury items) If the elasticity is equal to 1, it is referred to as unitary elastic If the elasticity is less than 1, it is referred to as inelastic (essential items) It is one thing to perform analysis on the supply and demand curves, but these curves can also be shifted because of outside sources. Whenever a curve is shifted, it is always with respect to the quantity at a certain price, meaning the curve will appear to move left or right along the x-axis. When altering a curve, it is best to isolate for the quantity variable and then make the adjustment. Increases cause the curve to move right, whereas decreases cause the curve to move left. There are many factors that would cause a shift in either curve. Examples include: Substitutes: goods that are essentially the same (coke / pepsi) Complements: goods that go together (left shoe and right shoe) Fear (demand decreases) Cheaper to produce (supply increases) When these curves shift, the market equilibrium point will shift accordingly. 1.2 Production Function Production function: the relationship between the physical output of a production process to physical inputs/factors The production function has the following form: A*S + B*S 2 C*S 3 where A > B > C and S is the input/factor/resource. The figure below shows the classic production function. Production function [Ref: fao.org] 5

7 Analysis can be performed to find the max product, the average product, max average product, marginal product, or max marginal product. With the parameters on the function fixed, a few key points can be derived. Max marginal product occurs when the double derivative of the total product equals 0 Max average product occurs when the average product equals the marginal product o At this point, a tangent line on the total product curve passes through the origin (has no y-intercept) Max total product occurs when the marginal product equals 0 This production function is a clear illustration of the law of diminishing marginal returns. This economic law states that if one input in the production is increased while all other inputs are held fixed, a point will eventually be reached at which additions of input yield progressively smaller, or diminishing, increases in output. All this to say that there is indeed a point in real world applications where adding more and more resources just doesn t do anything and you reach a max point. 1.3 Extra material not covered in this session Definitions (microeconomics, macroeconomics, finance, engineering, etc.) Infinitely elastic / completely inelastic Calculation of production function parameters Isoquants Diminishing marginal returns Returns to scale Production cost function and all accompanying calculations 6

8 Chapter 2: Principles of Accounting This chapter is a quick introduction to accounting principles such as financial statements and indicators and finally ends with depreciation models. 2.1 Financial Statements There are 3 different financial statements. 1) Statement of Net Income 2) Balance Sheet 3) Statement of Cash Flow Statement of Net Income The statement of net income shows the company s revenues and expenses for a particular period. An example is shown below. Income Statement Net sales 2150 Less: Cost of goods sold 600 Less: Depreciation 100 Less: Administrative and marketing expenses 150 Earnings before interest and taxes Less: Interest on long-term debt 500 Taxable income 800 Less: Income taxes 240 Net Income 560 Dividends paid 160 Addition to retained earnings 400 The income statement always has the revenue (sales) at the top, followed by all the expenses. The difference between the revenue and expenses is the taxable income. This amount is then exposed to taxes and a certain percentage of this amount needs to be paid out. What is left between the taxable income and the taxes is called the net income. The net income is then split up and used to pay out dividends and/or add to the retained earnings account Balance Sheet The balance sheet shows the current value of all accounts that exist within the company at a particular point in time. An example is shown below. 7