84 lines
2.2 KiB
Markdown
84 lines
2.2 KiB
Markdown
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# Price Elasticity
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We can calculate how our projected profits change when increasing or decreasing the price of our product.
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$|E_d| = \frac{\Delta Q(\%)}{\Delta p(\%)}$
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If $E_d > 1$ the price is **elastic**, when $E_d < 1$ the price is **inelastic** and when $E_d = 1$ the price is **unitary**.
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If we break the formula down, it is basically % Change in Quantity / % Change in price.
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**Example:**
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You sell 10.000 reams of paper at 100€/ream, you raise the price to 150€/ream and sell 7.000 reams.
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The Price Elasticity is now $\displaystyle \frac{\frac{QN-QI}{(QN+QI)/2}}{\frac{PN-PI}{(PN+PI)/2}}$
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$QN$= old Quantity
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$QI$= new Quantity
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$PN$= old Price
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$PI$= new Price
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So when we replace the variables with our numbers we get:
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$\displaystyle E_d = \frac{\frac{10000-7000}{(10000+7000)/2}}{\frac{100-150}{(100+150)/2}}$
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$\displaystyle E_d \approx −0.88$
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This means the price is inelastic. Meaning changes in price result in small changes to demand.
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**Moar Examples:**
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At a price of € 4 the quantity demanded of a particular good is
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100 units.
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1. Calculate the value of the price elasticity.
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2. Explain what type of demand.
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3. Plot the elasticity of demand
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In each case:
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a) If the price increases to 5 € and quantity demanded decreases to 90 units.
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b) If the price increases to 5 € and quantity demanded decreases to 50 units.
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c) If the price increases to 5 € and quantity demanded decreases to 75 units.
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d) If the price increases to 5 € and quantity demanded remains unchanged.
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e) If the price stays the same and the quantity demanded increases by 10 units.
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$\displaystyle a = \frac{\frac{100-90}{(100+90)/2}}{\frac{4-5}{(4+5)/2}} \approx -0.47$
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→ **Inelastic**
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$\displaystyle b = \frac{\frac{100-50}{(100+50)/2}}{\frac{4-5}{(4+5)/2}} = -3$
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→ **Elastic**
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$\displaystyle c = \frac{\frac{100-75}{(100+75)/2}}{\frac{4-5}{(4+5)/2}} \approx -1.28$
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→ **Elastic**
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$\displaystyle d = 0$
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→ **Perfectly Inelastic**
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$\displaystyle e = \frac{(100-110)/((100+110)/2)}{(4-4)/((4+4)/2)} = -\frac{2}{0} = Infinity$
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→ **Perfectly Elastic**
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**Example 3:**
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ppu = 30
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quantity = 300
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new ppu = 45
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new quantity = 225
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$\displaystyle E_d = \frac{(300-225)/((300+225)/2)}{(30-45)/((30+45)/2)} \approx |-0.71|$
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→ **Inelastic**
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