Following are portions of the demand curves of three...

Following are portions of the demand curves of three individuals for the water quality in a small pond. The water quality is expressed in terms of the parts per million (ppm) of dissolved oxygen (DO). Water quality improves at higher DO levels. The demand curves show the marginal willingness to pay of each individual (A, B, C). a. Complete the table. Find the aggregate marginal willingness-to-pay curve of these three people at each DO level. b. If the actual marginal cost of increasing DO is $$\$ 12$$, what is the socially efficient level of DO in the lake, assuming these three people are the only ones involved? (TABLE CAN'T COPY)

Following are portions of the demand curves of three individuals for the water quality in a small pond. The water quality is expressed in terms of the parts per million (ppm) of dissolved oxygen (DO). Water quality improves at higher DO levels. The demand curves show the marginal willingness to pay of each individual (A, B, C).
a. Complete the table. Find the aggregate marginal willingness-to-pay curve of these three people at each DO level.
b. If the actual marginal cost of increasing DO is $$\$ 12$$, what is the socially efficient level of DO in the lake, assuming these three people are the only ones involved?
(TABLE CAN'T COPY)

Key Concepts

Social Efficiency

Social efficiency occurs when the marginal social benefit, indicated by the aggregate marginal willingness to pay, equals the marginal cost of providing an additional unit of the good. This concept is used to determine the optimal level of investment in public goods—such as environmental quality—ensuring that resources are allocated where they yield the maximum net benefit to society.

Marginal Cost

Marginal cost is the additional cost incurred to produce one more unit of a good or to increase the quality by a marginal amount. In economic analysis, particularly in public goods or external benefit scenarios, it is important to compare the marginal cost with the aggregate marginal benefit to determine efficiency. Here, it is the cost of increasing the DO level in the pond.

Marginal Willingness to Pay

This concept refers to the additional amount an individual is willing to pay for one more unit of a good or an improvement, in this case, higher DO levels in the water. It reflects the value the person places on marginal changes and is depicted by segments of individual demand curves, demonstrating how much they value incremental improvements in quality.

Aggregate Demand Curve

The aggregate demand curve is constructed by summing the marginal willingness to pay of all individuals at each level of the good. It represents the total benefit derived by society from an additional unit of improvement. In the context of water quality, it involves adding up each person's willingness to pay for higher dissolved oxygen levels to get a collective or social measure of marginal benefit.

Transcript

0:00 All right.

00:01 So this has to do, this problem has to do with straight line demand and elasticity in accordance with that.

00:07 So to the right, i have drawn a graph and the demand curve that represents the table that was given to us in this problem.

00:16 And as you can see that this is a straight line demand curve.

00:19 This is because every time our demand changes by a certain amount, our price is changing with that.

00:25 So every time demand is changing by 100 bottles, our quantity is going up by a proportionate amount of 50 cents to that.

00:38 So now we have to solve for a elasticity for bottled water when the price rises from $1 to $1 .5.

00:50 So we reminding ourselves that elasticity of demand is equal to percent change.

00:56 In demand over percent change in price we'll first solve for our proportional change in the demand on top so we know that our demand is going down by 100 and then we're dividing that by the midpoint of the quantity change from 500 to 400 so we get 450 and this is all over our percent change in price so we know that our change in price is 0 .5 and that we're dividing it by the midpoint of $1 and $1 .5 so we get 1 .25.

01:32 And with this, now we can solve for our price, elasticity to demand.

01:37 So we just need to solve all these fractions.

01:40 And so i'll do how i usually do it here, but feel free to do it whatever suits you best.

01:51 2 .5 is you get about 5 over 9.

01:54 And we get about a price elasticity of about 0 .56.

02:01 And just as a reference, we'll mark this part of the curve, and this elasticity right here is 0 .56.

02:14 All right.

02:15 So now the problem is asking us to do the same thing, but for a price change of $2 to $3.

02:25 So now our quantity change is still the same.

02:30 It's 100.

02:30 However, the quantities that's changing from are different.

02:36 It's from 200 to 100 now.