This difference will not be confusing and you will

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This difference will not be confusing, and you will not be tripped up by this poten- tial pitfall. All you have to do is focus on the basic definition of elasticity in any given case, and keep in mind which variable is in the numerator (the “dependent” variable) and which variable is in the denominator (the “independent” variable). If the independent vari- able is on the vertical axis (as with price elasticities of supply and demand) then the flat- ter the function at a point, the higher is the elasticity of the dependent with respect to the independent variable. If the dependent variable is on the vertical axis (as with the elas- ticity of output with respect to labour inputs), then the steeper the function at a point, the higher is the elasticity of the dependent with respect to the independent variable. 2. Exercises 1. Using the Average Revenue functions from Question 1 of Module 5, calculate the elasticity of demand when Q = 10 tonnes: (a) using the formula = P/ ( m Q) from the text (pp. 105-6); (b) using the segment-ratio method, applied to the vertical axis. 2. Calculate the price elasticity of supply for the following functions when P = $10/unit and when P = $20/unit: (a) using the formula S = ( P/Q )(1/ m ), which is identical to MATH MODULE 6: ELASTICITIES M6-5 P F F C C A 1 S 1 A 2 A S 2 O O G G Q L Q Q(L) FIGURE M.6-4
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that for demand in the text; and (b) using the segment-ratio method, applied to the vertical axis. (a) P = –10 + Q (b) P = –10 + 2 Q (c) P = 0.5 Q (d) P = 2 Q (e) P = 4 + 0.5 Q (f) P = 4 + Q (g) P = 4 + 2 Q 3. If the vertical intercept of the tangent to a demand curve at a point C is $30/kg, give the values for and for Marginal Revenue at C if the price at C is: (a) $20/kg. (b) $25/kg. (c) $15/kg. (d) $5/kg. *4. The demand curve for Edible Veeblefetzers has a constant slope of –1/4, and when the elasticity of demand is –4, Marginal Revenue = $15/unit. What is the corre- sponding Total Revenue, in $? [Hint: TR = P x Q . What is Q ?] 5. You are given a function which (over the relevant range) has the form y = 30 + x . (a) If y stands for Price (in $/unit) and x stands for Quantity supplied (in units), then calculate the price-elasticity of supply for x = 30, 60 and 90. (b) If y stands for Quantity of Output (in units) and x stands for Labour inputs (in labour-days), then calculate the elasticity of Output with respect to Labour inputs for x = 30, 60, and 90. M6-6 MATH MODULE 6: ELASTICITIES
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