The weekly sales of Honolulu Red Oranges is given by #q=1116-18p#, how do you calculate the price elasticity of demand when the price is $31 per orange (yes, $31 per orange)?

"Price elasticity" gives the percentage change in quantity demanded in response to a one percent change in price.
Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price

http://www.investopedia.com/terms/p/priceelasticity.asp

#q = 1116 - 18p# Where q = demand and p = price.
at #$31/"orange"# we can calculate the changes based on a 10% change in price.

Initial: #q = 1116 - 18p#; #q = 1116 - 18 xx 31# ; #q = 558#
Change: #q = 1116 - 18p#; #q = 1116 - 18 xx 34.1# ; #q = 502.2#

Percent change in demand: #(558-502.2)/558 = 0.1#
Price elasticity = #0.1/0.1 = 1.0#

For a 50% change in price:
Change: #q = 1116 - 18p#; #q = 1116 - 18 xx 15.5# ; #q = 837#

Percent change in demand: #(558-837)/837 = -0.33#
Price elasticity = #0.33/0.5 = 0.667#

If the price elasticity of demand is equal to 0, demand is perfectly inelastic (i.e., demand does not change when price changes). Values between zero and one indicate that demand is inelastic (this occurs when the percent change in demand is less than the percent change in price).

When price elasticity of demand equals one, demand is unit elastic (the percent change in demand is equal to the percent change in price). Finally, if the value is greater than one, demand is perfectly elastic (demand is affected to a greater degree by changes in price).

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