Foundation of Economic Analysis 3250:600

Foundation of Economic Analysis3250:600 Instructor: Richard W. Stratton Meets: Thursday 5:20 – 7:50 pm CAS 136

Administration • This Week’s Assignments • Farnham Chapter 3 (Elasticity) • Homework 3 • Next Week’s Assignments • Review for Test 1 • Week 5 (September 28) • Test 1 • Then Week 6 • Farnham Chapter 5 (SR costs) • Farnham Chapter 6 (LR costs) • Homework 4 The University of Akron Decision Tree

Student Questions • Groups • Questions from last week? • Can group members help clarify? • Questions on reading for this week? • Can group members help clarify? • Share common unanswered questions The University of Akron

Decision Tree • Limiting cases • Revenue • Income elasticity • Cross-price elasticity Elasticity, def. Demand elasticity Determinants Calculate

Elasticity: definition • Elasticity measures the responsiveness of one variable to changes in a second variable • It is calculated as a “coefficient” or “pure number”. It has no units! • It is the percentage change in the first variable divided by the percentage change in the second variable. The University of Akron Decision Tree

Elasticity: types • How responsive is quantity demanded to changes in price? • How responsive is quantity supplied to changes in price? • How responsive is quantity demanded to changes in consumer income? • How responsive is quantity demanded to changes in the price of another good? Elasticity of demand Elasticity of supply Income elasticity Cross-price elasticity of demand The University of Akron Decision Tree

Elasticity of demand • How responsive is quantity demanded to changes in price? • Calculated as the percentage change in the quantity demanded divided by the percentage change in the price. ep =%change Qxd/ %change Px The University of Akron Decision Tree

Elasticity of demand • Calculated as the percentage change in the quantity demanded divided by the percentage change in the price. ep =%change Qxd/ %change Px ep = (Qxd2-Qxd1) / (Qxd2+Qxd1) (Px2-Px1) / (Px2+Px1) ep = (Qxd2-Qxd1) / (Px2-Px1) (Qxd2+Qxd1) / (Px2+Px1) The University of Akron Decision Tree

Determinants Individuals • Consider what factors influence your response to change in the price of a good. • Make a short list of those factors with examples. • Share in a group The University of Akron Decision Tree

Determinants From your text • The number and quality of substitutes • Percentage of consumers’ income spent on the good • The time period allowed for adjustment • The durability of the good The University of Akron Decision Tree

Determinants • The number and quality of substitutes • The more and the better the substitutes the response consumers • Less of a sacrifice • Percentage of consumers’ income spent on the good • The time period allowed for adjustment • The durability of the good The University of Akron Decision Tree

Determinants • The number and quality of substitutes • Percentage of consumers’ income spent on the good • The larger the percentage of the budget, the more responsive • It makes a difference! • The time period allowed for adjustment • The durability of the good The University of Akron Decision Tree

Determinants • The number and quality of substitutes • Percentage of consumers’ income spent on the good • The time period allowed for adjustment • The longer the adjustment period the more responsive • Allows time to find other goods and alter behavior • The durability of the good The University of Akron Decision Tree

Determinants • The number and quality of substitutes • Percentage of consumers’ income spent on the good • The time period allowed for adjustment • The durability of the good • Consumers tend to be more responsive to durable goods • Ability to postpone purchases The University of Akron Decision Tree

Elasticity of demand • Using the demand function from last week calculate elasticity of demand if price changes from • $10 to $9; $6 to $5; and $2 to $1 • Table • Graph • Algebraic function The University of Akron

Elasticity of demand (arc) • Table Price changes from $10 to $9 ep = %DQx / %DPx %DQx = (2 – 1)/(1+2) = 1/3 %DPx = (9 – 10)/(10+9) = -1/19 ep = (1/3) / -(1/19) = - (19/3) = - 6.33 The University of Akron

Elasticity of demand (arc) • Table Price changes from $6 to $5 ep = (DQx / DPx)(SPx / SQx) DQx/DPx = (6-5)/(5-6) = 1/-1 SPx / SQx = (11)/(11) = 1/1 ep = -(1/1) / (1/1) = - 1 The University of Akron

Elasticity of demand (arc) • Table Price changes from $6 to $5 ep = (DQx / DPx)(SPx / SQx) DQx/DPx = (10-9)/(1-2) = 1/-1 SPx / SQx = (3)/(19) ep = -(1/1) / (3/19) = - 0.158 The University of Akron

Elasticity of demand (arc) • Graph ep = - 6.33 ep = - 1 ep = - 0.158 The University of Akron

Elasticity of demand (arc) |ep| > 1 => elastic |ep| = 1 => unit elastic |ep| < 1 => inelastic The University of Akron

Elasticity of demand (point) • Algebraic function • Arc is • Point takes the inverse of the slope times Px / Qx ep = (Qxd2-Qxd1) / (Px2-Px1) (Px2+Px1) / (Qxd2+Qxd1) ep = (- 1) * (Px / Qxd) The University of Akron

Elasticity of demand (point) • Your textbook’s point formula is: ep = Px / (Px – a) • Px = 9 • Px = 6 • Px = 5 • Px = 1 ep = Px / (Px - 11) ep = 9 / (9 - 11) = - 4.5 ep = 6 / (6 - 11) = - 1.2 ep = 5 / (5 - 11) = - 0.83 ep = 1 / (1 - 11) = - 0.10 The University of Akron

Elasticity of demand (point) • Point elasticity formula takes the inverse of the slope times Px / Qx • Px = 9 • Px = 6 • Px = 5 • Px = 1 ep = (- 1) * (Px / Qxd) ep = (- 1) * (9 / 2) = - 4.5 ep = (- 1) * (6 / 5) = - 1.20 ep = (- 1) * (5 / 6) = - 0.83 ep = (- 1) * (1 / 10) = - 0.10 The University of Akron

Elasticity of demand (point) Let’s try some other functions Qxd = 15 - 3Px At Px = 2 ep = (1/slope) * (Px / Qxd) ep = (Px) / (Px - a) ep = (- 3) * (2 / 9) ep = (2.00) / (2.00 – 5) ep = (- 6 / 9) ep = (2) / (-3) ep = - 0.667 ep = -0.667 The University of Akron

Elasticity of demand (point) Let’s try some other functions Qxd = 20 - 2Px At Px = 5 ep = (1/slope) * (Px / Qxd) ep = (Px) / (Px - a) ep = (- 2) * (5 / 10) ep = (5) / (5 – 10) ep = (- 2 / (1/2)) ep = (5) / (-5) ep = - 1.0 ep = - 1.0 The University of Akron

Limiting cases • Both the arc and point elasticity formulae work with downward sloping demand functions • What of vertical and horizontal demand functions? The University of Akron

Limiting cases • Slope of a function is the rise over the run • Vertical (perfectly inelastic) • The rise is infinite • Thus the slope is infinite • Horizontal (perfectly elastic) • The rise is zero • Thus the slope is zero The University of Akron

Student Questions • Individually • What is the muddiest point about elasticity of demand? • In groups compare muddiest points • Are any in common? • Can group members help clarify? • List common unanswered questions • Share common questions The University of Akron

Revenue functions • Total Revenue = Price * Quantity • TR = Px * Qx • Average Revenue = TR / Qx • AR = TR / Qx = Px * Qx / Qx = Px • Is demand • Marginal Revenue = Additional Revenue per unit of output • MR = DTR / DQx The University of Akron

Revenue functions Returning to our example The University of Akron

Revenue functions ep elastic ep unit elastic ep inelastic MR AR = D The University of Akron

Revenue functions ep unit elastic ep elastic ep inelastic The University of Akron

Elasticity and Total Revenue • Total Revenue increases if • Revenue gained from price increase is greater than revenue lost by decrease in sales • Price increases over the inelastic portion of the demand curve The University of Akron

Elasticity and Total Revenue • Total Revenue increases if • Revenue gained from increased sales is greater than revenue lost by lower prices • Price decreases over the elastic portion of the demand curve • Total Revenue is maximized when demand elasticity is unit elastic The University of Akron

Student Questions • Individually • What is the muddiest point about the relationship between elasticity of demand and revenue? • In groups compare muddiest points • Are any in common? • Can group members help clarify? • List common unanswered questions • Share common questions The University of Akron

Income Elasticity • Income Elasticity measures how responsive the quantity demanded is to changes in consumer income. • Calculated as the percentage change in the quantity demanded divided by the percentage change in consumer income. eY =%change Qxd / %change Y The University of Akron

Income Elasticity • Remember that consumer income is a demand shifter • Inferior good => increase in consumer income leads to decrease in demand • Normal good => increase in consumer income leads to increase in demand The University of Akron

Income Elasticity • Inferior good => increase in consumer income leads to decrease in demand eY =%change Qxd / %change Y < 0 The University of Akron

Income Elasticity • Normal good => increase in consumer income leads to increase in demand eY =%change Qxd / %change Y > 0 The University of Akron

Income Elasticity Normal goods are often categorized as • Necessities • Luxuries eY > 0 The University of Akron

Income Elasticity What do we mean that a good is a necessity? • That everyone needs it? • That the amount needed is not very responsive to income • Thus while eY is positive, it is not very large 0 < eY < 1 The University of Akron

Income Elasticity What do we mean that a good is a luxury? • That not everyone can afford it • That the amount needed is responsive to income • Thus eY is positive and relatively large eY > 1 The University of Akron

Student Questions • Individually • What is the muddiest point about income elasticity? • In groups compare muddiest points • Are any in common? • Can group members help clarify? • List common unanswered questions • Share common questions The University of Akron

Foundation of Economic Analysis 3250:600