Question

Q1: The market for gold is represented by Q = 3P – 300 and Q = 8300 – 2P where Q is ounces of gold and P is the price of gold per ounce. a) What are the free market equilibrium price and equilibrium quantity of gold? b) The production of gold creates negative externalities. Give and explain two (and only two) specific and distinct negative externalities associated with gold production USING YOUR OWN WORDS. Unless you are very familiar with gold production, you will need to do some research to answer this question. c) Due to the negative externalities associated with gold production, the full social cost supply of gold is represented by Q = 2P – 500. What are the socially optimal equilibrium price and equilibrium quantity of gold? d) Why is the free market for gold inefficient? Explain in such a way that a layperson who does not know anything about economics would understand. In other words, DO NOT use terms such as total economic surplus and deadweight loss in your answer because a layperson would not know what they mean. e) What does the deadweight loss in the free market for gold equal? Show clearly how you arrived at your answer. f) What is one (and only one) government intervention that would make the free market for gold more efficient AND what impact does this government intervention have on the market?

Answer 1

Q1) The supply curve of gold: Q = 3P - 300, Demand curve of gold: Q = 8300 - 2P

a) So, to determine the free market equilibrium of gold, we need to equate the demand and supply curves, as the point of intersection gives us the equilibrium price and quantity of gold.

3P - 300 = 8300 - 2P , 5P = 8600, P = 1720/ounce

So, Q = 8300 - 2* 1720 = 4,860 ounces.

These are the equilibrium price and quantity under free market allocation.

b) Negative externality is referred to the adverse impact or the costs incurred by a third party due to the production/consumption of a good wherein the third party is not associated directly or involved in any economic transaction regarding the good. This cost to the third party or the society is not compensated by neither the producers nor the users of the good.

In this case, gold mining or production of gold creates negative externalities for the environment as well as people residing in the same area. Let's look at two of these:

1) Gold minining contaminates landscapes and water bodies, by the release of toxic substances like cyanide, mercury, cadmium, arsenic etc. which destroys vital ecosystems and has a critical impact on the environment.

2) Also, the toxic substances released through gold production, pollute main water sources and water lines of the human population living near these areas.This has yielded in huge cost of health to the people. Cadmium leads to liver diseases while arsenic can cause severe damage to the skin. So, an increase in gold mining and doing it callously results in loss of mankind and life.

c) Now, as in the case of negative externalities, the cost borne by the socety is greater than the private cost borne by the gold producers. The social cost supply of gold is given by the curve: Q = 2P - 500, So, when we equate this with the demand curve, we shall get the socially optimum equilibrium price and quantity,

2P - 500 = 8300 - 2P , 4P = 8800, P = 2,200/ ounce

Q = 2*2200 - 500 = 3,900 ounces

This is the price and quantity of gold which is socially optimum i.e. efficient for the society.

d) So, in simple terms, we see that the free market allocation of gold gives way to a lower price and a higher quantity as compared to the socially optimum price and quantity. This is because, the producers of gold do not consider this external cost borne by the society due to the negative externality, and tend to produce the quantity which will help to maximize their profits. So, they have an incentive to produce more as that will help them earn higher profits. However, when we consider this extra cost to the society, the quantity produced needs to be reduced so that the adverse impact on the society is reduced. As the society is not getting any compensation for this marginal cost borne by them, they would want to quantity of gold produced to be less and at the level which is optimum for the society as a whole. At the socially optimum quantity, the producers need to under-produce as compared to what they would have done in a perfectly competitive market. In free market, the demand curve is equal to private marginal benefit i.e. the benefit provided to the producers per unit produced which is equal to the social marginal benefit i.e. benefit provided to the society per unit produced. However, in case of marginal cost, the private marginal cost is depicted by the free market supply curve. However, the social marginal cost > private marginal cost, i.e. the cost incurred by the society is greater than the cost incurred by the producers. So, when this is considered, the supply curve shifts by this amount i.e. SMC - PMC = MD or marginal damage, this shift in the supply curve leads to a higher price and lower quantity i.e. the socially optimum level. This is why the free market allocation is not efficient.

d) First, let us suppose we know nothing about this externality, so market equilibrium will take place at the intersection of the supply and demand curves i.e. MPC and MPB curves. Notice that here, MPC = MSB as there is no external cost/benefit. This occurs at Q₁. This is the perfectly competitive equilibrium quantity = 4,860

The market surplus at Q₀ is computed by deducting total private costs from total private benefits = {(a+b+c+e+f) - (c+f)} = a + b + e

The social surplus at this equilibrium quantity is computed by deducting total social costs from total social benefits = a+b + c + e + f = aggegate net benefits. As, there is no positive externality, social benefit = private benefit.

Now, you can see in the graph, the MSC curve lies above the MPC curve for all the quantities because of the negative externality. So, the private cost is smaller than the social cost, the difference between MSC and MPC = external costs/marginal damage. Total social costs = b + c + d + e + f ,

Total private cost = b + e + d, The social surplus at Q₀ is is equal to the total social benefits - total social costs,

Social surplus = {(a+b+c+e+f) -(b+c+d+e+f)} = a-d,

Now, if we look at the socially optimum quantity, Q₁ = 3,900, the market surplus would be lower at this level by triangle 'e'. The market surplus at Q₁ = {(a+b+c) - (c)} = a + b, Now, total social benefit at Q₁ = a + b + c, total social cost = b + c,

So, social surplus at  Q₁ = a + b + c - (b+c) = a ,

So, we see moving to a quantity Q₁ lesser than Q₀, we have increased the social surplus. So, even though the market surpus is reduced, there is an increase in the social surplus by the area 'd'. So, 'd' is the deadweight loss from being at free market level of production. So, this was inefficient for the society.

e) If the market is left unregulated and let the producers and consumers set the quantity and price, the society is worse off on the whole. So, the government needs to intervene and regulate to make the society better off.

So, this can be done by the govt leving a tax on the production of gold, equal to the value of the external cost, this will make the producers from reducing their supply and the market equilibrium quantity will be equal to socially efficient quantity. This will lead to a increase in the social surpus and fall in deadweight loss.