Question

Price (dollars) Total revenue (dollars)

1.00 110

1.25 125

1.50 125

1.75 100

Tim sells hot dogs from a truck in the park. The table above shows his daily total revenues at four different prices. Between which two prices is the demand for hot dogs

a. inelastic? b. unit elastic? c. elastic?

thank you for your help

Answer 1

Solution:

We are given the following:

Price (in $s)	Total Revenue (in $s)
1.00	110
1.25	125
1.50	125
1.75	100

Note that total revenue = price*quantity

So, on taking log and differentiating with respect to time, we know that:

Percentage change in total revenue = percentage change in price + percentage change in quantity

Furthermore, law of demand states that price and quantity are inversely related, that is if price of a good increases, it's demand decreases and vice-versa.

If increase in price causes increase in total revenue, it means demand is inelastic, as percentage (positive) change in price is with higher than the percentage (negative) change in quantity. In other words, increase in price doesn't seem to be affect demand much strongly. If increase in price causes no change in total revenue, it means demand is unitary elastic, since there is equal percentage change in price and quantity. Finally, if total revenue decreases with increase in price, the demand is elastic as price change has a strong impact on demand and thus, percentage decrease in quantity surpasses the percentage increase in price, resulting in lower total revenue.

Considering all this, and the table above, we observe that

a) As price of hot dogs increase from $1.00 to $1.25, total revenue increases from $110 to $125, so between these mentioned prices, demand for hot dogs is inelastic.

b) As price of hot dogs increase from $1.25 to $1.50, total revenue remains same (that is unchanged) at $125, so between these mentioned prices, demand for hot dogs is unit elastic.

c) As price of hot dogs increase from $1.50 to $1.75, total revenue decreases from $125 to $100, so between these mentioned prices, demand for hot dogs is elastic.