A 5% fall in price of a good leads to 10% rise in its demand A consume...
A 5% fall in price of a good leads to 10% rise in its demand. A consumer buys 40 units of a good at a price of 10 per unit. At a price of 12 per unit, he would buy 36 units. This is calculated by taking the percentage decrease in price (10%) and dividing it by the percentage increase in demand (10%). The result is 1, meaning for every 1% decrease in price, demand increases by 1%. Therefore, if the price is increased by 2, the demand will decrease by 20%. 40 units divided by 1.2 (20% decrease) is 36 units.
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A 5% fall in price of a good leads to 10% rise in its demand A consume...
Given:
- A 5% fall in price leads to a 10% rise in demand.
- The consumer buys 40 units of the good at a price of $10 per unit.
To Find:
- How many units will the consumer buy at a price of $12 per unit.
Calculation:
We can solve this problem using the concept of price elasticity of demand. Price elasticity of demand measures the responsiveness of the quantity demanded to a change in price.
Step 1: Calculate the price elasticity of demand:
The price elasticity of demand formula is given by:
Elasticity = (% change in quantity demanded) / (% change in price)
In this case, we know that a 5% fall in price leads to a 10% rise in demand. So the percentage change in quantity demanded is 10% and the percentage change in price is -5% (fall in price).
Elasticity = (10% / -5%) = -2
Step 2: Use the price elasticity of demand to calculate the new quantity demanded:
The price elasticity of demand tells us how much the quantity demanded will change in response to a change in price. In this case, with an elasticity of -2, a 1% increase in price will lead to a 2% decrease in quantity demanded.
Since the price has increased from $10 to $12 per unit (a 20% increase), we can calculate the percentage change in quantity demanded as follows:
Percentage change in quantity demanded = (20% * -2) = -40%
Step 3: Calculate the new quantity demanded:
We know that the consumer originally buys 40 units of the good at a price of $10 per unit. Therefore, the percentage change in quantity demanded is relative to the original quantity:
New quantity demanded = (40 units * -40%) = -16 units
Since negative quantities do not make sense in this context, we can ignore the negative sign and take the absolute value:
New quantity demanded = 16 units
Answer:
The consumer will buy 16 units of the good at a price of $12 per unit.
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