The efficient quantity of CDs to produce is the quantity for which the marginal cost of making an additional copy equals the marginal benefit to the user. Once the CD has already been produced, the added cost of one more CD is just the copying cost, and the added benefit is the marginal willingness to pay of the person using the CD.

So the efficient quantity of CDs should be the quantity for which the (red) marginal cost curve intersects the (green) demand curve [which represents consumers' marginal willingness to pay]. In the figure, those two curves intersect at a quantity of 10.

Since it actually costs $10 to produce and record the CD, it also should be checked that it is worthwhile to produce it. (The alternative would be simply not to produce the CD, and not to make any copies.) It's worthwhile to produce the CD if the total consumer surplus to demanders, minus the cost of copying the CDs, exceeds the cost of producing and recording. In the figure, the consumer surplus minus the copying cost is the area of the triangle, between the green demand curve and the red marginal cost curve. The triangle has an area of (0.5)(10)(1)=50, which exceeds the cost of producing the CD.

So the efficient policy is to produce the CD, and to make 10 (thousand) copies.

The cost of construction is irrelevant here to the issue of efficiency. The arena has already been built. The construction costs are sunk costs (even if the arena's owner is still paying the interest).

The efficient quantity of people to let into the game is the quantity for which the marginal benefit to the last person let in to the game equals the marginal cost of letting the person in.

Now as long as attendance is below capacity, the marginal cost of letting another person in is zero : attending the game is a non-rival good.

Since the equation of the demand curve for the game is Q=15-p, therefore the height of the demand curve hits zero at a quantity of 15. If we let 15 thousand people into the arena, the marginal willingness to pay of the last person is zero. Since the capacity of the arena is 20>15, then it is efficient to let 15 thousand people attend the game : everyone who has a positive marginal willingness to pay. The price, therefore, should be 0 : everyone who wants to watch the game should be allowed to attend the game, since attending the game is a non-rival good so long as the number of people who want to attend is less than the capacity.

If a monopoly can price discriminate perfectly, then it will provide the good up to the point at which the last customer's marginal willingness to pay for the last unit equals the marginal cost of providing the good.

If the good is non-rivalrous, the marginal cost of providing it to one more person is 0. Therefore, the price-discriminating monopoly will provide the good to everyone who wants to consume it. That is the efficient quantity to make available, if the good is non-rivalrous.

The monopoly will charge admission (since the good is excludable) : it will charge a high price to people who have a high willingness to pay.

Because it can price discriminate perfectly, it is not concerned with its marginal revenue : selling more units does not require the monopoly to cut its price across the board, to all buyers.

The perfectly price discriminating monopoly still might not be able to make a profit. Its total revenue is just the area under the aggregate demand curve for the non-rivalrous good. If that area is less than the cost of actually producing the good, then the monopoly cannot make a profit from producing the good, even if it could extract all the consumer surplus from buyers.

The "Samuelson rule" for the efficient quantity to provide of a non-rival good, is that the sum of all consumers' marginal benefits should equal the marginal cost of producing another unit. That is, the demand curves should be added vertically, and the efficient quantity is the quantity at which this vertically-summed demand curve intersects the marginal cost curve.

Here the marginal cost of producing each episode is $10,000,000. So the efficient quantity of episodes is the quantity at which the sum of all consumers' marginal willingness to pay equals $10,000,000.

If there are 10 million identical viewers, the sum of everyone's marginal willingness to pay equals $10,000,000 if (and only if) each viewer's marginal willingness to pay is $1.

So the efficient number of episodes is the number at which each viewer's marginal willingness to pay (the height of her demand curve) equals $1. From the table, that's a quantity of 4 episodes.

The "Samuelson rule" for the provision of a public good says that, if the quantity provided is efficient, then the sum of all people's marginal willingness to pay for a little more of the public good should equal the marginal cost of producing a little more.

The question stated that the efficient quantity of the public good was 20 units, and that the marginal cost was 5. That means that the sum of everyone's marginal willingness to pay must equal 5, if the quantity produced is 20.

So the average of all 10 people's willingnesses to pay must equal 0.5 (since the sum of all 10 people's marginal willingness to pay must equal $5). But that does not mean that each person must have a willingness to pay of 0.5. People need not be identical. It certainly could be the case that, at a quantity of 20, some people have a marginal willingness to pay which is greater than 0.5, and some have a marginal willingness to pay which is less than 0.5. As long as the marginal willingness to pay of the 10 people sums up to $5, then the quantity provided of the public good is efficient.

The efficient quantity is the quantity for which the sum of the three people's marginal willingness to pay is 12.

The marginal willingness to pay is the height of a person's demand curve. So, for example, at a quantity of 1, person #1's marginal willingness to pay is 7, since she demands 1 unit at a price of 7.

Since everyone's demand curve slopes down, the higher the the quantity, the lower is each person's marginal willingness to pay. At a quantity of 2, person #1 is willing to pay 6, person #2 is willing to pay 7, and person #3 is willing to pay more than 7, so that the sum of the three people's marginal willingness to pay is 20 or more, which is greater than the marginal cost. So an output of 2 is less than the efficient level. At a quantity of 6, person #1's marginal willingness to pay is 2, person #2's is 3, and person #3's is 4, so that the sum of their marginal willingness to pay is 9, less than the marginal cost of production (which is 12). So an output of 6 is greater than the efficient level.

The efficient level must lie somewhere between 2 and 6 : going through the numbers in the chart shows that at an output of 5, person #1's willingness to pay is 3, person #2's is 4, and person #3's is 5, so that the correct answer is a quantity of 4, since then the sum (3+4+5) of the three people's willingness to pay equals the marginal cost.

The net income of an oil well operator is the revenue from the yield of her oil well, minus the cost of drilling. So if her oil well produces q barrels of oil, her net income will be 50q-1,000,000, since oil sells for $50 a barrrel, and each well costs $1,000,000.

Free entry by firms means that as long as net income is positive, there will be more firms willing to enter, and drill oil wells. In equilibrium, the net income of each oil well must be 0 : only then will there be no pressure for entry to or exit from the industry.

So, with free entry, in equilibrium 50q-1,000,000=0, or q=20,000. A yield of 20,000 barrels per well means that firms' oil revenue just covers the cost of drilling the well.

When will the yield of each well equal 20,000 barrels? The yield q per well equals 1,000,000 divided by the number of wells, since the 1,000,000 barrels of oil in the pool are shared equally by all firms. So the yield per well will equal 20,000 if there are 50 wells. Free entry by oil firms results in 50 wells being drilled.

In this case, there is no benefit to drilling more wells. Increasing the number of oil wells does not, in this example, increase the total yield from all the wells : it just divides it more ways.

So if there were 4 wells, each well would produce 250,000 barrels. Increasing the number of wells from 4 to 5 would mean that each of the 5 wells would yield 200,000 barrels. In each case, the total yield of all the wells is just the quantity of oil in the pool, 1 million barrels.

So drilling more wells does not increase the value of the output from the oil field. But it costs money to drill more oil wells.

Therefore, in this example the most efficient policy is to drill as few wells as possible. The aggregate net income of oil well operators is just $50,000,000 (the value of the total oil production) minus the cost of drilling the wells.

Drilling only 1 well will maximize this net income, since it minimizes drilling ocsts without lowering revenue.

Free entry to the village commons means that farmers will have an incentive to raise more chickens, as long as they can make a profit. Free entry will drive down the profit from raising chickens on the commons to zero.

So in equilibrium, the profit should be zero from raising a chicken on the commons. The profit from raising a chicken is w-3, where w is the weight of the chicken : the farmer gets $1 per kilo, but had to pay $3 to get the chicken.

Therefore, free entry implies that in equilibrium, the weight of each chicken on the village commons must be 3 kilos. The table indicates that this will happen if there are 6 chickens in total grazing on the commons.

The total income from chicken farming is (w-3)n, where n is the number of chickens on the commons, and w is the weight of each chicken. (That's because farmers get $1 per kilo from selling their chickens).

The table indicates that the weight per chicken decreases with the number of chickens. Specifically, here w=9-n. So the net income from having n chickens on the commons is (w-3)n=(9-n-3)n=(6-n)n=6n-n². This total income increases at first with the number of chickens (it equals 5 when there is one chicken, and 8 when there are 2 chickens), but eventually starts to decrease (it equals 8 when there are 4 chickens, and then 5 when there are 5 chickens).

The highest value for total net income is achieved when there are 3 chickens, each weighing 6 kilos, for a total net income of 9. [This can be seen by calculating using the data in the table, or by taking the derivative of 6n-n²].