Suppose the demand for artichokes (Qa) given as Qa=120-P. a) What is the price elasticity of demand?

Question

Suppose the demand for artichokes (Qa) is represented by the equation Qa = 120 - P. 
a) What is the price elasticity of demand for artichokes?
b) If the price of Qa is increased from $10, how will this affect the quantity of artichokes sold and the total expenditure by consumers on artichokes?
c) At what price, if any, is the demand for artichokes infinitely elastic?

Anonymous · Accepted Answer

a) price elasticity of demand = dQ/dP * P/Q
dQ/dP = -1
So, price elasticity of demand = -1 * P/Q = -P/Q
The actual value of this expression will be different at each price, which is what we would expect since we know that elasticity varies along a demand curve.
b) When P = 10, Qa = 120 - 10 = 110
So, price elasticity of demand = -10/110 = -1/11
This number (in absolute value) is less than 1, so at this point, we would say that demand is relatively inelastic.  This means that consumers are not very responsive to price.  Therefore, increasing the price would result in the total expenditure by consumers on artichokes increasing.
c) To find the point, if any where demand is infinitely elastic, we want to find a price where -P/Q = infinity.  A fraction approaches infinity as the denominator approaches zero.  So at what price is Qa = 0?  
0 = 120 - P
P = 120

Anonymous

Suppose the demand for artichokes (Qa) given as Qa=120-P. a) What is the price elasticity of demand?

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