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53-Maths_behind_PED

# 53-Maths_behind_PED - along a linear demand curve 4 Total...

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The mathematics of price elasticity of demand 1. Show how formula a, given below, for price elasticity of demand can also be written in the form shown in formula b Formula a Formula b PED = % q PED = p q % P q p 2. a) A linear demand curve can be expressed in the form q = a – bp . Using first principles of calculus from mathematics, we know that the slope of that demand function can be written as q/ p. Give another way in which the slope of the demand function can be expressed, using the information given about the equation of the demand function. b) Using the information from question 1 and question 2a, show how the PED can be expressed in the form shown below: -bp _ a – bp 3. Explain how the formula given in question 2b can be used to show that PED varies
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Unformatted text preview: along a linear demand curve. 4. Total revenue can be calculated using the formula R = pq. Assume that in a particular market with a linear demand curve, a change in price is given as p + ∆ p and the associated change in quantity is given as q + ∆ q. a) Write down a formula for the new level of total revenue, R new b) Write down a formula for calculating the change in total revenue as a result of the change in price c) Write down a formula for calculating the rate of change in revenue per change in price. d) Explain how you can use this formula to demonstrate how total revenue changes as price changes along a linear demand curve...
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