Price 1 is 50, price 2 is 38.78.

Quantity 1 is 100, quantity 2 is 169.
solve the price elasticity of demand.
what if our goal is to decrease price by 14%
what if our goal is to raise quantity from 169 to 300 by how much percentage we should decrease price? -2=%Q/P

To solve for the price elasticity of demand, we can use the formula:

Price elasticity of demand = (Percentage change in quantity / Percentage change in price)

First, let's calculate the percentage change in quantity. We start by subtracting the initial quantity (Q1) from the final quantity (Q2) and divide it by the initial quantity Q1. Then, we multiply the result by 100 to convert it to a percentage.

Percentage change in quantity = ((Q2 - Q1) / Q1) * 100
= ((169 - 100) / 100) * 100
= 69%

Next, let's calculate the percentage change in price. We use the same approach as above, subtracting the initial price (P1) from the final price (P2), dividing it by the initial price P1, and multiplying by 100 to convert it to a percentage.

Percentage change in price = ((P2 - P1) / P1) * 100
= ((38.78 - 50) / 50) * 100
= -22.44%

Now, we can calculate the price elasticity of demand:

Price elasticity of demand = (Percentage change in quantity / Percentage change in price)
= 69% / -22.44%
≈ -3.07

The price elasticity of demand in this scenario is approximately -3.07. Since the result is negative, we can conclude that the goods in question are considered price elastic, meaning that a change in price would result in a relatively larger change in quantity demanded.

Now, let's address the second part of your question. If the goal is to decrease the price by 14%, we can calculate the new price by subtracting 14% from the current price (P2).

New price = P2 - (14% of P2)
= 38.78 - (0.14 * 38.78)
= 33.37

To calculate the percentage decrease in price, we use the formula:

Percentage decrease in price = ((P2 - New price) / P2) * 100
= ((38.78 - 33.37) / 38.78) * 100
≈ 13.9%

So, to decrease the price by 14%, we would need to decrease it by approximately 13.9%.

Finally, let's calculate the percentage decrease in price required to raise the quantity from 169 to 300 using the formula -2 = %Q/P. Rearranging the formula, we get:

%Q/P = -2

Since we have the initial quantity (Q) and want to find the percentage decrease in price (%P), we can substitute the values into the formula:

%Q/P = ((Q2 - Q1) / Q1) * 100 / ((P2 - P1) / P1) * 100

Plugging in the given values:

-2 = ((300 - 169) / 169) * 100 / ((P2 - P1) / P1) * 100

Now, let's simplify the equation:

-2 = 77.22 / ((P2 - P1) / P1)

To solve for (P2 - P1) / P1, we can rearrange the equation:

(P2 - P1) / P1 = 77.22 / -2

Simplifying further:

(P2 - P1) / P1 ≈ -38.61

Therefore, to raise the quantity from 169 to 300, the percentage decrease in price required is approximately 38.61%.