Suppose the income elasticity of demand for a food is 0,5 and the price elasticity of demand is -1,0. Suppose also that Felicia spends $10,000 a year on food, the price of food os $2 and her income is $25,000

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Well, well, well, we have a mathematical feast going on here! Let's see what we can cook up with these numbers.

First, let's tackle the income elasticity of demand, which is 0.5. Income elasticity measures how sensitive the demand for a product is to changes in income. With an income elasticity of 0.5, it means that for every 1% increase in income, the demand for this food will increase by 0.5%.

Now, let's move on to the price elasticity of demand, which is -1.0. Price elasticity measures how sensitive the demand for a product is to changes in price. With a price elasticity of -1.0, it means that for every 1% increase in price, the demand for this food will decrease by 1%. A bit grumpy, huh?

Onto Felicia, who spends $10,000 a year on food. With a price of $2 per food item, we can deduce that she purchases 10,000 / 2 = 5000 food items in a year. That's a lot of snacking!

Now, let's dig into her income, which is $25,000. Since we know the income elasticity is 0.5, we can calculate the percentage change in demand caused by her income. A 1% increase in her income would result in a 0.5% increase in her food demand. So, 1% of $25,000 is $250, and 0.5% of $10,000 is $50. This means that her demand for food would increase by $50 if her income increased by $250. Guess that extra income doesn't go all into food after all!

As for the price elasticity, with a price elasticity of -1.0, a 1% increase in price will result in a 1% decrease in demand. Since the price is $2, the price increase per item would be 1% of $2, which is $0.02. That might not seem like a lot, but if Felicia purchases 5000 food items, the decrease in her demand caused by the price increase would be 1% of 5000, which is 50. If we assume a linear relationship, this means that if the price of food increases by $0.02 per item, Felicia's demand would decrease by 50 items. Yikes!

So, there you have it! Felicia's food purchasing habits are influenced by her income elasticity of 0.5 and the grumpy price elasticity of -1.0. Remember, numbers can be fun, but don't forget to share a laugh along the way!

To calculate the quantity demanded, we can use the formula:

Quantity Demanded = (Income Elasticity of Demand) * (Percentage Change in Income) * (Initial Quantity Demanded)

Since the income elasticity of demand for food is 0.5, and Felicia's income is $25,000, we can calculate the percentage change in income as follows:

Percentage Change in Income = (New Income - Initial Income) / (Initial Income) * 100

Percentage Change in Income = ($25,000 - $25,000) / ($25,000) * 100 = 0%

Now we can substitute the values into the formula:

Quantity Demanded = 0.5 * (0%) * (Initial Quantity Demanded)

Since the percentage change in income is 0, the quantity demanded will remain the same as the initial quantity demanded.

Now let's calculate the initial quantity demanded, using the formula:

Initial Quantity Demanded = Total Expenditure / Price

Felicia spends $10,000 a year on food, and the price of food is $2:

Initial Quantity Demanded = $10,000 / $2 = 5,000 units

Therefore, the quantity demanded is 5,000 units.

To calculate the change in quantity demanded due to changes in income (income elasticity of demand), you can use the following formula:

Income Elasticity of Demand = (% change in quantity demanded) / (% change in income)

Given that the income elasticity of demand for food is 0.5, we can use this formula to solve for the percentage change in quantity demanded.

0.5 = (% change in quantity demanded) / (% change in income)

Next, let's calculate the percentage change in income. We know that Felicia's income is $25,000, and we need to determine the percentage change.

Percentage change in income = (New income - Old income) / Old income

Percentage change in income = ($25,000 - $25,000) / $25,000 = 0

Since the percentage change in income is zero, the equation becomes:

0.5 = (% change in quantity demanded) / 0

Since we are dividing by zero, we cannot calculate the percentage change in quantity demanded with this equation. Therefore, we cannot determine the specific change in quantity demanded due to changes in income alone.

Now, let's move on to calculating the price elasticity of demand. The formula to calculate price elasticity of demand is similar to the income elasticity of demand formula:

Price Elasticity of Demand = (% change in quantity demanded) / (% change in price)

Given that the price elasticity of demand for food is -1.0, we can use this formula to solve for the percentage change in quantity demanded.

-1.0 = (% change in quantity demanded) / (% change in price)

We know that the price of food is $2, but we need to determine the percentage change in price. Let's say the new price is $x.

Percentage change in price = (New price - Old price) / Old price

Percentage change in price = ($x - $2) / $2

Now, we will calculate the percentage change in quantity demanded using the given price elasticity of demand:

-1.0 = (% change in quantity demanded) / [($x - $2) / $2]

To calculate the percentage change in quantity demanded, rearrange the equation:

(% change in quantity demanded) = -1.0 * [($x - $2) / $2]

Now that we have the equation, we need to consider Felicia's current expenditure on food. She spends $10,000 a year on food, and the price of food is $2. We can use this information to calculate the current quantity demanded using the formula:

Quantity demanded = Expenditure / Price

Quantity demanded = $10,000 / $2 = 5000 units

To calculate the new quantity demanded due to changes in price, we can rearrange the percentage change equation:

New quantity demanded = (1 + (% change in quantity demanded)) * current quantity demanded

Now, substituting the values we have, we can solve for the new quantity demanded:

New quantity demanded = (1 + {-1.0 * [($x - $2) / $2]}) * 5000 units

Unfortunately, we cannot determine the specific quantity demanded due to changes in price without knowing the new price (represented by $x).