Problem Set 2Sol - 1 ECONOMICS 100 NOTES ON PROBLEM SET #2...

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1 ECONOMICS 100 NOTES ON PROBLEM SET #2 (Elasticity; Market Interventions) 1. Elasticity 1.1 Calculating Elasticity Consider the demand schedule given by the equation: p = 10 – 1q, and the points A (p = $8; q = 2) and B (p= $6 and q = 4). The diagram below shows this. Now calculate the point elasticity at A, and the arc elasticity between A and B. P 10 A ($8, 2) B ($6, 4) 10 Q 1.1 Arc Elasticity: Between A and B: ? q = 2 Avg q = 3 ? q = -2 Avg p = 7 For Arc Elasticity, use mid-point formula to compute % changes: Arc Price Elasticity of Demand = - % ? q / % ? p = - [2/3 / -2/7] = 7/3 Point Elasticity of Demand: Point Elasticity of Demand = - [ ? q / ? p] * p/q At point A: p = 8; q = 2. [ ? q / ? p] = run / rise or 1/slope of D = -1. So, E D = - (-1) * 8/2 = 4
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2 1.2 Elasticity Concepts What do the following statements suggest about the elasticity of the commodities in question: a) I love peanut butter; to me a day without peanut butter is not a day! Statement suggests that consumer is not sensitive to price changes i.e., relatively inelastic price elasticity of demand (value of E D less than 1). b) As the price of calculators fell (due to improved technology) the revenues of my company, a producer of calculators, grew dramatically. Technology changes shifted S to the right along a given D schedule, causing p to fall. As p fell along the D schedule from A to B, TR rose. Implication: relatively elastic price elasticity of demand – as p fell, q rose more than enough to cause the product of p times q to rise (value of E D greater than 1). P S 1 A S 2 B D Q c) Now that I'm an executive, I've tossed out all my polyester suits. Now that I’m an executive, my income (I) has presumably risen. I won’t be buying polyester any more. So, as I rises, quantity demanded of polyester falls. This is the concept of income elasticity of demand E I = %? q / %? I. In this case, it has a value of less than zero (i.e., negative), and we have an inferior good.
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3 d) I've noticed that every time the price of tea has risen, the price of coffee has risen too (shortly thereafter). As the price of tea rises, the Demand for coffee, a substitute, will rise. Assuming a negatively-sloped D and positively-sloped S for coffee, we expect that the price of coffee will rise too when D increases. (We ignore the feedback on the tea market!). Key concept here is the notion of substitutes, which in turn should suggest the cross price elasticity of demand, as follows: Ey/x = % ? q of coffee / % ? p of tea. This value is positive for substitutes. e)
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This note was uploaded on 01/16/2011 for the course ECO 100 taught by Professor Indart during the Fall '08 term at University of Toronto- Toronto.

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Problem Set 2Sol - 1 ECONOMICS 100 NOTES ON PROBLEM SET #2...

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