5. The effect of negative externalities on the optimal quantity of consumption A

Question

5. The effect of negative externalities on the optimal quantity of consumption Aa Aa Suppose that a steel manufacturing plant in San Francisco dumps toxic waste into a nearby river, creating a negative externality for those living downstream from the plant. Producing an additional ton of steel imposes a constant marginal external cost of $350 regardless of the level of production. There is no marginal external benefit from steel production, so the private benefit equals the benefit to society The following table summarizes the private benefit and marginal cost for each level of output from the steel manufacturing plant. Quantity of Steel (Tons) Private Benefit Marginal Cost 900 700 500 300 200 150 50 150 350 450 550 650 The following graph shows the demand curve and the marginal cost curve for steel. (Note: The demand for the plant's steel is the same as the full-benefits demand curve.)

Explanation / Answer

To find the exact quantity we use two point formula to find out slope and intersept
we will find the slope only at the intersection

You want to find the equation for a line that passes through the two points:
(2,500) and (3,700).
First of all, remember what the equation of a line is:

y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down".
A large slope means the line goes up or down really fast (a very steep line).
Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through.
Let's call the first point you gave, (2,500), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=2 and y1=500.
Also, let's call the second point you gave, (3,700), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=3 and y2=700.

Now, just plug the numbers into the formula for m above, like this:

m=(700 - 500)/(3 - 2)
or...

m=200/1
or...

m=200
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=200x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(2,500). When x of the line is 2, y of the line must be 500.
(3,700). When x of the line is 3, y of the line must be 700.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=200x+b. b is what we want,
the 200 is already set and x and y are just two "free variables" sitting there.
We can plug anything we want in for x and y here, but we want the equation for
the line that specfically passes through the two points (2,500) and (3,700).

So, why not plug in for x and y from one of our (x,y) points that we know the
line passes through? This will allow us to solve for b for the particular line
that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(2,500). y=mx+b or 500=200 × 2+b, or solving for b: b=500-(200)(2). b=100.
(3,700). y=mx+b or 700=200 × 3+b, or solving for b: b=700-(200)(3). b=100.
See! In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points
(2,500) and (3,700)
Replacing x=q and y=p
is

p'=200q+100..........(1) New supply curve

Like this we can find slop for old demand and supply
p=100q+50............before tax supply Curve
p=-200q+1100........Demand Curve

Efficient quantity
Demand=Supply
100q+50=-200q+1100
q=1050/300
p=100(1050/300)+50=350+50=400

Market quantity because of tax

-200q+1100=200q+100
q=1000/400=2.5
p=200(2.5)+100=600

B)
For producing market efficient production government should provide subsidies of 350 per ton of steel

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