Between any two points (x1, f(x1)) and (x2, f(x2)) is the slope of the line through the two points, and this line is called the

Find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is th

Aleks [24]

Answer:

$7812.5million

Step-by-step explanation:

From the question, the demand quantity <em>D(x) is 410-x </em> and the supply quantity <em>S(x)=160+x.</em> We determine the equilibrium quantity by equating the Demand quantity and the Supply quantity i.e

Hence the equilibrium quantity is 125.

Next we determine the equilibrium price. This can be obtain by just substituting the equilibrium quantity into either the demand quantity or the supply quantity. I prefer using the Demand quantity.

Equilibrium price= $410-125=285\\$ .

Next we write the expression for the Consumer Surplus

$CS=\int\limits^q_0 {D(x)} \, dx -pq$

where <em>p</em> and <em>q </em> are the equilibrium price and equilibrium quantity respectively.

By substituting values we have

$CS=\int\limits^q_0 {(410-x)} \, dx (285)(125)\\$

$CS=/410x-\frac{x^{2} }{2} /^{125}_{0} \\$

By carrying out simple arithmetic we arrive at

$CS=(51250-7812.5)-(285)(125)\\CS=$7812.5million$ .

To determine the producer surplus, we use the expression below

$PS=pq-\int\limits^q_0 {S(x)} \,dx\\$

Hence if we substitute values we arrive at

$PS=(285)(125)-\int\limits^q_0 {(160+x)} \,dx\\PS=(285)(125)-[(160x-\frac{x^{2} }{2})]^{125}_{0}$ .

By simply simplification we arrive at

$PS=(285)(125)-(20000+7812.5)\\PS=35625-27812.5\\PS=$7812.5million$

7 0

4 years ago

The image shows the angles formed by a pair of scissors. When the scissors are closed, m∠1 = 0°. As the scissors are opened, the

Serga [27]

Angle 3 is a vertical angle of angle 1 and will always be identical to what angle 1 is.

Angle 2 and angle 4 are supplementary angles to angle 1 and will always be the difference between 180 and what angle 1 is.

For example if angle 1 was 45 degrees, angle 3 would also be 45 degrees and angle 2 and angle 4 would be 180-45 = 135 degrees.

4 0

3 years ago

joan has a piece of material for making a costume she needs to cut it as shown what is the angle measure of the piece left over?

skelet666 [1.2K]

We need to see the problem. show a picture

8 0

3 years ago

Why do countries, make alliances, in wartime? please someone help me!

Maru [420]

Answer:

Most of the time, it is because they need the military aid or the resources that a certain country needs. That's kinda what the UN is all about is aiding each other in times of war

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Using the table below, find the mean and median of the set of data.

Schach [20]

The mean of the data set is 81.6.

The median of the data set is 80.

The mean is the average of a data set. Therefore,

Mean = (70 x 2 + 75 x 8 + 80 x 6 + 85 x 3 + 90 x 9) / 28 = 81.6.

Hence,

mean = 81.6

<h3>What is a median?</h3>

Median is a statistical measure that determines the middle value of a dataset listed in ascending order .

Therefore,

28 / 2 = 14

median = 80 + 80 / 2 = 160 / 2 = 80

learn more on mean and median here: brainly.com/question/28052298

#SPJ1

5 0

2 years ago