Danny "Dimes" Donahue is a neighborhood’s 9-year-old entrepreneur. His most recent venture is selling homemade brownies that he bakes himself. At a price of $1.50 each, he sells 100. At a price of $1.00 each, he sells 300. a. Is demand elastic or inelastic over this price range? . b. If demand had the same elasticity for a price decline from $1.00 to $0.50 as it does for the decline from $1.50 to $1.00, would cutting the price from $1.00 to $0.50 increase or decrease Danny’s total revenue? .

a. To determine whether the demand for Danny's brownies is elastic or inelastic, we need to understand the concept of price elasticity of demand. Elasticity measures the degree to which the quantity demanded of a good responds to a change in price. If the quantity demanded changes significantly with a small change in price, the demand is said to be elastic. If the quantity demanded changes very little with a large change in price, the demand is said to be inelastic.

The price elasticity of demand (PED) is calculated using the following formula:

PED = (% Change in Quantity Demanded) / (% Change in Price)

Now let's calculate the PED for Danny's brownies:

First, we determine the percentage change in quantity demanded:

Change in quantity = New quantity - Original quantity 

= 300 - 100 

= 200 

Percentage change in quantity demanded

 = (Change in quantity / Original quantity) * 100 

= (200 / 100) * 100 

= 200%

Next, we determine the percentage change in price:

Change in price = New price - Original price

 = $1.00 - $1.50

 = -$0.50 

Percentage change in price 

= (Change in price / Original price) * 100

 = (-$0.50 / $1.50) * 100 

= -33.33%

Now, we calculate the PED:

PED = 200% / -33.33% 

= -6 (Ignoring the negative sign which indicates the inverse relationship between price and quantity demanded)

A PED greater than 1 (in absolute value) means the demand is elastic. Since Danny's PED turned out to be 6, which is much greater than 1, we can conclude that the demand for his homemade brownies is elastic over this price range.

b. Since we've established that the demand is elastic, we know that the percentage change in quantity demanded is greater than the percentage change in price. Therefore, when the price decreases, the total revenue (Price x Quantity Sold) increases because the increase in quantity demanded more than compensates for the decrease in price.

If the demand has the same elasticity for a price decline from $1.00 to $0.50 as it does for the decline from $1.50 to $1.00, cutting the price from $1.00 to $0.50 would likely increase Danny's total revenue. This is because the quantity sold would increase by a higher percentage than the decrease in price, assuming that the products remain elastic at this new price range.