Social welfare functions

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Social welfare activities (2 points) Let P stand for pollution in the social welfare function SW = UAl(XAl,w*P) + UJo(XJo,w*P), with Al and Jo both exposed. This SW function represents what standard (efficiency, safety, or sustainability)? What would the SW function for each of the other standards look like? Explain in detail.

Because the SW function implies the presence of negative externalities, it represents the efficiency standard. The function suggests that Al and Jo's utilities are provided based on the consumption of an x, common good; this implies that the function is generally dependent on the choices of individuals in society. As shown, consuming X results to emergence of an external cost that is not part of the transaction cost; thereby production of X triggers in the rise in environmental population which in turn impacts the society’s members; this therefore results to negative externalities associated with efficiency standards.

For the sustainability standard, the social welfare function would include the use of “fairness weight” to make sure there is fairness of the coming generations. This is how the function will look like:

SW = w * UAl(XAl, PAl) + UJo(XJo, PJo)

Whereby w represents the weighing number that is adequate to cover for the effects of increase in John’s consumption on Rachel. In which case, the increase in one’s happiness in the present cannot rise at the expense of future generations.

For safety standard, there is need for utilization of a fairness weight with regards to pollution. Here is the social welfare function:

SW = UAl(XAl, w*PAl), + UJo(XJo)

In the above function, using a big enough weight (w) would fail to counter the process of production versus the negative effects resulting from pollution therein.

Q2. Opportunity Cost

The concept of opportunity cost is referring to the benefit that a person foregoes at the expense of another. In other words, the concept refers to an alternative that has been given up in the process of arriving at a decision (Investopedia 2017). In this regard, people and businesses usually go for those opportunities that are of high return.

Application explanation

a) There are more parks per square mile in rural areas than in urban areas

The rural area in terms of the cost of land and the benefit it has to businesses is low as compared to the urban areas and also land is in plenty. Having more parks per square mile in the rural areas therefore is cost effective as compared to having the same in the urban areas where the demand for land is high and putting parks will be underutilizing the land.

b) Protesters and activists tend to be younger (on average) than the typical worker

Note: Time is also considered a scarce resource

Protesting is an activity that requires energy and the younger generation are having this energy as compared to the older generation. In this sense, for the old people getting involved in protest will be of high cost as they can be subjected to ill health afterwards that will be costly in the long run. For the younger generation, the act of protesting is not necessarily affecting them health wise hence they do not lose as much as the older generation do.

Question 3: Q3. Efficient markets – Supply and Demand - Consumer and Producer surplus (5 points) Suppose you are interested in the economic effects of the 2015 Gold King Mine waste water spill on the tourism industry along the Animas River. You have estimated a pre-disaster demand and supply functions for boat rides on the Animas River:Demand: P= 1000 – 10 QDemandSupply: P = 40 QSupply

a) Construct a graph representing the pre-disaster boat ride industry including the equilibrium price and quantity. (Label your axes!)

The equilibrium prices and the prices represented as;


b) Calculate the consumer and producer surplus in this industry before the spill, as well as the Total surplus. Following the spill, there is an outpouring of media discussing the high concentrations of dangerous material in the water.

Consumer surplus =

The producer surplus=

Therefore, the total surplus is the summation of consumer surplus and producer surplus which is,

c) Show on your graph what would happen to the demand function. Which determinant of demand is responsible for this change? You re-estimate the demand function following the spill and find that the newdemandfunctionlookslike: P=500−10 QDemand

d) What are the new equilibrium price and quantity?

Since the two are at equilibrium, the new equilibrium price and quantity is at 400

e) What is the new total surplus?

The new total surplus is calculated using the new producer and consumer surplus


Total surplus is given by;

f) What is the change in total surplus caused by the Gold King Mine waste water disaster?

The change in the surplus is;

Therefore, there is no change in the total surplus.

g) Does your answer to (f) provide a comprehensive description of the effect this environmental disaster? Why or why not?

It does not give a comprehensive change because irrespective 0f change in producer surplus, the total surplus still remains the same.

Q4. Efficient markets – Supply and Demand - Consumer and Producer surplus

a) Explain and illustrate what will happen to the supply of cars if there is an improvement in car tire manufacturing technology. How does price, quantity, producer surplus, and consumer surplus get affected? (You can use letters to label surfaces on the graph, as we did in class)

The demand for the supply of cars in the event that their manufacturing technology has been improved will increase. Consequently, the pricing of such cars will shoot to match the improved quality. Hence at the beginning the supply will need to be increased due to increased demand. Consequently, the increase in price of the vehicles will affect the demand as only those capable of meeting the new set prices will be able to purchase the newly improved vehicles and this will reduce the quantity. When plotted in a graph the there will be reduction in quantity with increase in price but an increase in supply with improvement in quality. The graph below shows the explanation.

In the above graph the increase in prices shows a decrease in supply and vise verse. On the other hand, the supply is seen to be directly proportion to both price and quantity when the quality has been improved. At the equilibrium point, the supply and demand for the cars will have reached a point where they are equal. At this point the there is no consumer nor producer surplus.

b) Do we know for sure if producer surplus will increase or decrease?

It is possible to know the possibility of the producer surplus or not when the pricing is manipulated. The increase in price leads to producers having a lot of surpluses while the decrease in price results in consumers surplus.

c) What if the city builds new bike paths, what will happen to the demand for cars? d) What if the city taxes gasoline more heavily?

The building of new bike paths by the city might not impact on the demand for the cars because the cars can be used for long-distance travels hence their demand will still be as initially. The high taxing of gasoline may result in a slight decrease in the demand as people will tend to use alternative means like public transport.

Q5. Market Failures

What are the 4 sources of market failure? Explain how and why they are market failures and give real-world examples (not used in class). Which 2 market failures are the most prevalent in Environmental Economics?

The sources of market failures are as follows (Chand, n.d.).

Incomplete markets: a condition where there are missing items under perfect competition and they cause failure because there is no way of equating their private and social benefits as well as costs. Lack of certain commodities leads to unsatisfied customers and consequently market failure.

Common property resources: the common ownership of properties coupled with open access may lead to wasteful exploitation as it leads to waste and inefficiency. For example, common fishing grounds may lead to overfishing resulting to market failure.

Externalities: the presence of externalities in production and consumption result in market failure because the market will not be offering price for the services rendered. For example, high supply of cereal as a product will lead to underpricing that leads to market failure.

Negative externalities of production: in the event that the production of commodity or service gets to affect many firms, the social marginal cost increases more than marginal benefit leading to market failure. For example, a big company producing local goods will kill similar small businesses.

Among the above failures, the most common in the environmental economics are common property resource and negative externalities of production.

Q6. Externalities (4 points)1. You have estimated demand and supply functions for plastic bags: Demand: P= 1000 – 10 QDemand Supply: P = 40 Q Supplywhere quantities are expressed in tons of plastic bags, and prices are in $

a) Construct a graph representing the plastic bag industry including the equilibrium price and quantity. (Label your axes!) The real impact of plastic bag litter is felt on wildlife both in the marine environment and in rural areas. Tens of thousands of whales, birds, seals and turtles are killed every year from plastic bag litter in the marine environment as they often mistake plastic bags for food such as jellyfish. Plastic marine debris has substantial economic impacts on coastal communities, documented in the millions of dollars spent in the form of clean-ups or lost in decreases in tourism. Economists have evaluated that each additional ton of plastic bag creates an external cost of $300.

b) How is this additional costs translated onto the previous graph? What additional curve can you add?

Having the increment I supply by the $300. The new supply equation will be;

So at equilibrium, the supply and demand equal, therefore;

The demand shifts to the right.

c) Calculate the efficient prices and quantities. Will the free market over-supply or under-supply plastic bags? Explain why in words.

The supply price is given by;

At equilibrium, both the supply and demand are equal, therefore;

d) What is dead-weight loss (you do not need to calculate it, just explain in words)? Show it on the graph.

The free market will over-supply the plastic bags. This is due to the need to match up to the uprising shift in demand.

The loss is incurred by the company due to the additional costs spent is clean ups of the environment and the probable government policy of the reduced production and use of the plastic bags.

Q7. Tragedy of the Commons

What is the "tragedy of the commons" and in what instances will it arise?

The tragedy of the commons refers to a theory of a situation occurring within a shared resource when it is being exploited by individuals acting independently (Investopedia, 2017). This situation arises when a given resource is owned by many people without restrictions for use, for example, a grazing field that is owned communally. In such a scenario, some individual may just decide to over-graze their livestock leading to exploitation of the field.


Chand, S. 8 Major Causes of Market Failure (Explained With Diagram). The Next Generation Library. Retrieved 21 September 2017, from

Investopedia, I. (2017). Tragedy Of The Commons. Investopedia. Retrieved 21 September 2017, from

Investopedia. (2017). Opportunity Cost. Investopedia. Retrieved 21 September 2017, from

May 17, 2023

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