Elasticities, Government and Market outcomes

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Department
Economics for Management Studies
Course
MGEA02H3
Professor
All Professors
Semester
Summer

Description
ELASTICITY Knowledge Summary: 1. Elasticity: measures the % change in Q for a 1% change in P E = % change in Q / % change in P 2. Formulas: - Ed = - dQ/dP x P/Q - Es = dQ/dP x P/Q - dTR/ dQ = P (1 – 1/Ed) given P and Ed, want to know the change in TR for one unit change in Q - dTR / dP = Q (1 – Ed) given Q and Ed, want to know the change in TR for one unit change in P 3. Elasticity of supply and demand can be used to calculate the share of taxes between consumers and suppliers - Ed / Es = Supplier’s share of taxes / Consumer’s share of taxes - Consumer’s share of taxes + Supplier’s share of taxes = tax imposed by government - From the relationship, we can see that the more elastic the demand, the less tax burden the consumer will bear. 4. Elasticity is the measure of responsiveness of one thing to another. Elastic: absolute value > 1, Inelastic: absolute value < 1, Unitary Elastic: absolute value = 1 Perfectly Elastic: absolute value = infinity, Perfectly Inelastic: absolute value = 0 5. In a downward sloping demand curve, the top half is inelastic while the bottom half is elastic. A supply curve is elastic if it starts from the y axis, inelastic is it starts from the x axis and unitary elastic if it starts from the origin. Summary of Questions to be asked 1. Find Elasticity:  Price Elasticity of Demand: measure of responsiveness of price to a change in quantity o PED= % Change in Quantity % Change in Price  Price Elasticity of Supply: measure of responsiveness of price to a change in supply o PED= % Change in Quantity % Change in Price  Income Elasticity: measure of responsiveness of income to a change in quantity o IED= % Change in Quantity % Change in Income 2. Elasticity and Total Expenditure/Revenue  Total Expenditure = Price * Quantity  The change in total expenditure on a product in response to a change in price depends on elasticity of demand  Elastic demand: price increase/decrease = total expenditure decrease/increase  Inelastic demand: decrease/increase = total expenditure decrease/increase 3. Incidence of Tax  Greater PED and lesser PES mean a greater burden of tax on producer.  Greater PES and lesser PED mean a greater burden of tax on consumer.  PED=O/PES=Infinity o All of the burden of the tax would go to the consumer because demand is unresponsive to change in price (PED)  PED=Infinity/PES=0 → The entire burden falls on the producer  PED=1/PES=1 → The burden is shared equally between the producer and consumer  General Rule: the inelastic party gets most of the burden Given PED and PES and a tax, BS/SS = E /E S ID other words, the ratio of the buyers’ share to the sellers’ share of a tax will be equal to the ratio of the elasticity of supply to the elasticity of demand. Related Exam Questions Questions from 2011 Midterm Question 5, 6,7,11,12,16,17,18,19,22 and 23 Answers 5) The sellers will bear all the tax because the supply curve is relatively inelastic compared to the perfectly elastic demand curve. There will be some excess burden since supply is inelastic. The correct answer is (B). 6) Since total expenditure decreases when the price of a good rises when the demand curve is elastic, the correct answer is (E). 7) All three statements are true by definition. The correct answer is (G). 11) You know that BS/SS = E /E .SIn Dther words, the ratio of the buyers’ share to the sellers’ share of a tax will be equal to the ratio of the elasticity of supply to the elasticity of demand. We know that this ratio is 5.0/2.5 or 2/1. That means, that if we have a $1 tax and we split it into 3 parts, two parts will be paid by buyers and and 1 part by sellers, or $0.67 by buyers and $0.33 by sellers. The correct answer is (F). 12) The total revenue for the industry is the same as the total expenditure by consumers, so this question asks how total expenditure changes as quantity changes. We can calculate dTE/dP = d(P∗Q)/dP. This requires the product rule, so dTE/dP = [dP/dP ∗ Q] + [dQ/dP ∗ P] or [dQ/dP ∗ P] + Q. We can transform this derivative by multiplying by Q/Q so we get Q([dQ/dP ∗ P/Q] + Q/Q). We can usefully rewrite this as dTE/dP = Q(1 + ED). We can calculate this derivative as 6000(1 + 1/3) = $8000. This is an approximation of the effect for a one-unit change in P. 12) The correct answer is (D). 16) We can analyze the effects of the tax either on the demand curve or the supply curve (because the results will be identical). Using the supply side, we have S + T = 52 = .02Q, so that 52
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