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)?

Question

Eva Adamson · Accepted Answer

See below. The high "constant" means that the demand is unit elastic for small changes, and inelastic for higher price changes.

Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price provides the percentage change in quantity demanded in response to a one percent change in price. Investopedia's webpage on price elasticity #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# Demand is perfectly inelastic (i.e., it does not change when prices change) if the price elasticity of demand is equal to zero. Demand is inelastic (i.e., it changes when the percent change in price is less than the percent change in demand) if the price elasticity of demand is between zero and one. Demand is unit elastic (the percent change in demand is equal to the percent change in price) when price elasticity of demand equals one. Demand is perfectly elastic (demand is affected to a greater degree by changes in price) if the value is greater than one. Read more: Price Elasticity Of Demand https://tutor.hix.ai Follow us: Investopedia on Facebook

Isaiah Anthony · Answer

undefined Price elasticity of demand (PED) can be calculated using the formula:

$$ \text{PED} = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Price}} $$

First, calculate the quantity demanded when the price is $31 per orange:

$$ q = 1116 - 18p $$
$$ q = 1116 - 18(31) $$
$$ q = 1116 - 558 $$
$$ q = 558 $$

So, when the price is $31 per orange, the quantity demanded is 558 oranges.

Now, to calculate the percentage change in quantity demanded, use the formula:

$$ \% \text{ Change in Quantity Demanded} = \frac{Q_{\text{new}} - Q_{\text{old}}}{Q_{\text{old}}} \times 100\% $$

$$ \% \text{ Change in Quantity Demanded} = \frac{558 - 1116}{1116} \times 100\% $$
$$ \% \text{ Change in Quantity Demanded} = \frac{-558}{1116} \times 100\% $$
$$ \% \text{ Change in Quantity Demanded} = -50\% $$

Since the price is $31 per orange, and a $1 decrease in price would be the percentage change in price:

$$ \% \text{ Change in Price} = \frac{1}{31} \times 100\% $$
$$ \% \text{ Change in Price} \approx 3.23\% $$

Now, plug the percentage changes into the PED formula:

$$ \text{PED} = \frac{-50\%}{3.23\%} $$
$$ \text{PED} \approx -15.5 $$

So, the price elasticity of demand when the price is $31 per orange is approximately -15.5.