In Ozone, California people all have the same tastes and they all like hot tubs.

Question

In Ozone, California people all have the same tastes and they all like hot tubs. Nobody wants more than one hot tub but a person with wealth $M will be willing to pay up to $.01M for a hot tub. The distribution of wealth in Ozone is as follows. The number of people with a wealth greater than $W for any given W is approximately 1,000,000/W. The price elasticity of demand for hot tubs in Ozone California is:
(a) - 0.1
(b) - 0.01
(c) - 1
(d) - 0.4
(e) None of the above.

(Please show work or explain. i already have the answer. just need to know how to solve it)

Explanation / Answer

Initial Case

Assume that initial case , price of hot tub is , P

then only people with, 100P wealth will buy (since a person with wealth $M will be willing to pay up to $.01M for a hot tub )

Initial demad (D1) = no. of people with 100P income = 1000000/100P = 10000/P

Second Case

Assume now the price is doubled , i.e. 2P

then only people with wealth of 200P will buy hot tum

Second Demand (D2) = 1000000/200P = 5000/P

Price elasticity of demand = % change in demand/% change in Price

% change in demand = (D2-D1)*100/D1 = (-5000/P)*100/(10000/P) = -50

% change in price = (2P-P)*100/P = 100

so, elasticity = -50/100 = -0.5

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