Quiz 2. Elasticity ANS

# Quiz 2. Elasticity ANS - dP s dQ s = a dQ s dP s = 1 a...

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ECON 201 Shomu Banerjee ELASTICITY QUIZ ANSWERS (a) The equation for an inverse demand function is given by P d = a Q d where a > 0 is a constant. Calculate the price elasticity of demand, ε . The slope of the inverse demand is dP d dQ d = " a ( Q d ) 2 , so dQ d dP d = " ( Q d ) 2 a . Substitute into the elasticity formula " = dQ d dP d # P d Q d : = # ( Q d ) 2 a \$ P d Q d = # ( Q d ) 2 a \$ ( a / Q d ) Q d = -1. (b) The equation for a linear inverse supply function is given by P s = aQ s , where a > 0 is the slope of the supply curve (i.e., this inverse supply passes through the origin with slope a ). Calculate the price elasticity of supply , s . Since
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Unformatted text preview: dP s / dQ s = a, dQ s / dP s = 1/ a . Substituting in the elasticity formula, s = dQ s dP s # P s Q s = 1 a # P s Q s = 1 a # aQ s Q s = 1. (c) Show that if a linear inverse supply function has a positive vertical intercept, then it is elastic, i.e., ε s > 1. Hint: Write the inverse supply function as P s = aQ s + b , where b > 0 is the positive vertical intercept. Substituting in the elasticity formula, we get s = dQ s dP s # P s Q s = 1 a # ( aQ s + b ) Q s = 1 + b aQ s > 1....
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