Supply and demand functions for butter pecan ice cream

In summary, the equilibrium quantity for butter pecan ice cream is 125 10-gallon tubs and the equilibrium price is $50. To find these values, the supply and demand functions were set equal to each other, resulting in an equilibrium quantity of 125 and an equilibrium price of $50. To verify these values, they can be plugged back into the equations and checked. In the second conversation, the cost-benefit model for removing pollutants is given by y=(6.5x)/(102-x). To find the cost of removing each percent of pollutants, the values of 0%, 80%, and 100% can be substituted into the equation for x to find the corresponding costs.
  • #1
gillgill
128
0
Let supply and demand functions for butter pecan ice cream given by
p=S(q)= 2/5q and p=D(q)=100 - 2/5q
where p is the price in dollars and q is the number of 10-gallon tubs.
Find the equilibrium quantity and the equilibrium price.
do i just set them equal to each other??

2/5q=100-2/5q
equilibrium q=125
equilibrium p=50
are these answers correct?
 
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  • #2
Yes, they are correct.

You didn't really need someone to tell you that did you? Just put p= 50,q= 125 into the equations and see if they are correct:
p= (2/5)q= (2/5)(125)= 2(25)= 50 is correct and
p= 100- (2/4)q= 100- 50= 50 is correct.
 
  • #3
coz someone told me that they are not correct...so i just want to make sure...
thanks...i have another question
Suppose a cost-benefit model is given by
y=(6.5x)/(102-x)
where y is the cost in thousands of dollars of removing x percent of a certian pollutant.
a) find the cost of removing each percent of pollutants:
0%, 80%, 100%
do i just sub in 0, 0.8 and 1 in the equation where it has x?? or u sub in 1, 80 and 100?
 

1. What is a supply and demand function?

A supply and demand function is a mathematical representation of the relationship between the quantity of a product (in this case, butter pecan ice cream) that producers are willing to supply and the quantity that consumers are willing to purchase at different price levels.

2. How do you create a supply and demand function for butter pecan ice cream?

To create a supply and demand function for butter pecan ice cream, you would need to gather data on the quantity of ice cream that producers are willing to supply at different prices and the quantity that consumers are willing to purchase at those prices. This data can then be plotted on a graph to determine the relationship between supply and demand.

3. What factors influence the supply and demand of butter pecan ice cream?

The supply and demand of butter pecan ice cream can be influenced by a variety of factors, including the price of ingredients, production costs, consumer preferences, and competition from other ice cream flavors.

4. How do changes in supply and demand affect the price of butter pecan ice cream?

If there is an increase in demand for butter pecan ice cream, the price will likely increase as producers try to meet the higher demand. On the other hand, if there is a decrease in demand, the price may decrease as producers try to sell their excess supply. Similarly, if there is a decrease in supply (due to higher production costs, for example), the price may increase, and if there is an increase in supply, the price may decrease.

5. Can supply and demand functions for butter pecan ice cream be used to predict future prices?

Yes, supply and demand functions can be used to make predictions about future prices of butter pecan ice cream. By analyzing trends in supply and demand data, economists and businesses can make informed decisions about pricing and production levels. However, it is important to note that unforeseen events or changes in consumer preferences can also impact prices, making it difficult to accurately predict future prices with 100% certainty.

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