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I have a exercise with the corresponding answer, but i don't get it:

Suppose there's a better wheather this year and the size of the harvest of soy increased a 60%. The demand curve for soy did not change. The price of the soy dropped a 20%. We can conclude that the elasticity of demand is -3.

Is this true? Under what circumstances? Why? Thank's a lot!

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Example

if p = -1%

and the production increase is +2%

elasticity is -2

[2/-1 = -2]

Our exercise

if this is true

when p = -20%

and production is 60% more

elasticity is -3

[60/-20 = -3]

To sell the 60% more the price has to decrease, if it decreases of 20%, the ratio among products sold (+60%) and price decrease (-20%) is equal to -3.

So, elasticity is the ratio among variation in quantity (60%) and variation in price (-20%) = -3.

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  • $\begingroup$ I understand, but the exercise states that the harvest increased 60%, meaning that the supply would be larger by 60%, not the demand. So, i can interpret as a displacement of the supply curve. If the price drops, means that the demand did not raise 60%, but less. That is what confuses me, because the answer is Elasticity of demand is -3. $\endgroup$ – S. Cow Jul 12 '17 at 12:44
  • $\begingroup$ Yes, it is a bit confusing, maybe, but I interpreted it in this way: as the production raised, to sell the difference (+60%) the price had to go down of 20%. So if when (in the first example) the production goes up of 2% and the price goes down of 1%, the elasticity is -2, doing the same process, when production increase of 60% and price decrease of 20% (for there is more product on the market, to stimulate more consumer to buy it you have to lower the price) the elasticity is 60/-30 = -3. I think that this means that to make the consumer buy all the new production, price went down 20%. $\endgroup$ – Giovanni Python Jul 12 '17 at 15:52
  • $\begingroup$ Sorry, I meant 60/-20 = -3 (increase in production / decrease of price) ... you have an elasticity of minus 3. You have to compare the variation of production /60%) with the variation of the price (-20%). From the demand the inclination of the curve is negative, of course, as the price goes to the opposite direction of the production. If the production goes up, the price (being the demand the same) goes down so that people buys more of that good. $\endgroup$ – Giovanni Python Oct 7 '17 at 4:34
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These changes (-20%, +60%) are too large to use point elasticity methods (which are accurate for small changes in price, like 1%). The claim seems to be based on an arc elasticity formula instead, measured between the original Q and the new quantity, which is (1.6)*Q. The two types will be equal only if elasticity is constant everywhere, which is very unlikely to be the case!

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