Trade and welfare

Who bought the first iPhone?

Technology, early adopters and consumer surplus

Source: Associated Press

Steve Jobs introduced the first iPhone in 2007. Compared with today's smart phones, it was fairly primitive. The screen was a tiny 3.5 inches and with low resolution. The camera was also not impressive--stand alone point-and-shoot cameras of the days gave much better pictures. The software and operating system were both limited and in the beginning buggy, and there was no app store. You were limited to the apps that Apple decided to include on the phone.

Just as importantly, at a time when most phones in the US might cost 200 dollars, the iPhone initially had a price of 650 dollars, though this was dropped to 400 dollars after a few months.

Nonetheless, the iPhone was revolutionary. The iPhone got rid of the physical keyboard, and with its relatively large screen covering most of the surface, it was the first phone that made accessing the internet somewhat user friendly.

Nonetheless, many probably thought it would be a good idea to wait for the next iteration or two before they spent a lot of money on an iPhone. And they were right. Subsequent iPhones became much more powerful.

And yet there were also those that rushed to buy the first iPhone, even standing in long lines to get the first out of the factory. Within tech, we call those that jump on new, sometimes imperfect technologies, as early adopters. Early adopters are often as much interested in testing out the novelty of a technology as they are in the utility that the technology can provide.

These early adopters are important in technological advance. Imagine if no one had bought that first, expensive iPhone, and Apple had decided that the whole iPhone project was a dud? We should be happy that people are different and have different preferences for adopting technology.

This lesson is about how microeconomists take into account different preferences among consumers and producers in the way they model a market. And we will show how economists use the idea of varying preferences to think about a somewhat theoretical concept called consumer surplus in a market.

Consumer surplus

The first two panels in the figure above represent the demand curve of two inviduals (or we could think about it as certain groups.) If we think about this as the market for iPhones, then perhaps the first panel represents a group of early adopters (red) that are willing to buy the iPhone even when the price was high. The next group will wait.

Initially, the price is so high that no one is willing to buy the product. Then there is also no consumer surplus.

Press the Reduce market price button a few times. You notice now that the the price now drops far enough that the first Early Adopters begin to buy. The triangle that gets filled in represents the consumer surplus of the those in group 1 that think it is worth the price to buy the product (the early adopters). The consumer surplus is the difference in between what the market price is and how much each of these consumers would be willing to pay.

Continue to press the Reduce market price button until people in the yellow group begin to buy the product. Now we see a yellow triangle that represents the consumer surplus among this group.

In the third panel, we can see how we sum the consumer surplus horizontally in order to calculate out the consumer surplus for the entire market.

Now imagine that instead of two or three individuals or groups, we think about summing over many hundreds or thousands of individuals or groups. Then we can imagine we get an aggregated demand curve that is almost completely smooth.

Producer surplus

In this figure we see the individual supply curves for producers. iPhones are kind of a bad example since only one company makes iPhones. So let us go back to our example of cars.

We start with a situation where the market price is so low that no company is willing to make and sell a car.

Press the Increase market price button a few times. When the price comes high enough, then we see that VW is willing to make and sell some cars. The green triangle represents VW's producer surplus: The difference between the market price and VW's marginal cost of producing a car.

Press the Increase market price button a few times more until Toyota begins to produce and sell cars. Higher prices often have the effect of getting more producers into a market. The little triangle again represents the Toyota's producer surplus.

In the third panel, we see producer surplus summed horizontally across all producers. Again we can imagine a case where instead of two producers we had many in which case we would a supply curve that is nearly smooth.

Total social surplus

When we have summed up over many individual demand curves (marginal willingness to pay), then we end up with a smooth demand curve for the entire market. In the same way, when we sum up many individual supply curves (marginal costs) we end up with a smooth market supply curve.

So here is the big question we want to answer: if our goal is to maximize the total amount of surplus in the market (and we don't care about the distribution of that surplus between consumers and producers), what should the price be and how much production should there be?

The elegant answer to this question is that the maximum social surplus (sum of producer and consumer surplus) is at the free market equilibrium, where total demand meets total supply!

To convince ourselves of this, let us consider an alternative. In the figure, press the - quantity button a few times. In this situation, we have a demand curve that lies above the supply curve. We can interpret this as having individuals that are willing to pay to buy an extra good for the market price (and would gain consumer welfare in the process) and there are producers that are willing to produce and sell extra goods for the markets price and would earn producer welfare in the process. Thus we could increase production and sales and get more total social surplus. And this would continue until we again are at the equilibrium.

So why would we ever be in a situation where consumers and producers are not at the free competition equilibrium? Here there are many possibilities: Regulation and taxes, market power and monopoly. We will discuss these in upcoming lessons.

Now press + quantity a few times until we have a quantity that is bigger than the equilibrium quantity. We have now drawn in a red triangle. This represent the societal loss. If these goods were sold at the market price, then the consumers that bought them would lose since the market price is more than the willingness to pay. At the same time, the marginal cost of producing each unit beyond the equilibrium quantity is also higher than the market price, also leading to a loss.

But why in the world would a consumer buy a product that costs more than it is worth to that person? Why would a company sell a product at a loss?

Usually, in a well-functioning market, these transactions would take place (though we could probably think of many exceptions.)

But let us say that a third party gets involved - the government. For example, the government announces a new policy giving a generous subsidy to buy electric cars. This subsidy leads consumers to buy electric cars that otherwise would not have been sold, and producers to make electric cars that otherwise would not have been produced.

This does not mean that the subsidy is bad or necessarily wasteful. The pollution from traditional automobiles also represents a cost to society (what economists call a externality), and thus it may be worth while to give an extra subsidy. But it does come at a cost, and economists are often wary of such subsidies.

The lesson from this should not be that completly free markets are always best or that government intervention is bad. Instead, we use free market equilibrium as a type of benchmark in order to evaluate the costs of, for example, a subsidy. Thereafter we have to decide whether those costs are worth it.

Quiz

Problems

1.) Demand functions for bananas for three individuals are as follows:

$$X_E^1 = 10 - p_B$$ $$X_E^2 = 15 - p_B$$ $$X_E^3 = 10 - 2p_B$$

a.) If the price is \(p_B = 3\) how many bananas are bought in total?

b.) What is the total consumer surplus? (You can assume that you need to buy whole bananas)

a.) We can calculate from the demand functions:

$$X_E^1 = 10 - p_B = 10-3 = 7$$ $$X_E^2 = 15 - p_B = 15 - 3 = 12$$ $$X_E^3 = 10 - 2p_B = 10 - 6 = 4$$ $$total = 23$$

b.) Consumer surplus is the sum of the differences between what a consumer is willing to pay and the market price.

To get marginal willingness to pay, we can rewrite the demand functions:

$$X_E^1 = 10 - p_B $$ $$p_B^1 = 10-x_B^1 $$

So for consumer 1, the willingness-to-pay for the first bananas is:

$$10-x_B^1 = 10-1 = 9$$

The consumer surplus becomes:

$$9-3 = 6$$

The marginal willingness-to-pay and surplus for the next banana is:

$$10-x_B^1 = 10-2 = 8 => 8-3 = 5$$

Continuing on in this way we get:

$$6+5+4+3+2+1+0 = 21$$

Consumer 1 gets 21 in consumer surplus.

We continue with Consumer 2:

$$p_B^2 = 15-x_B^2$$

Surplus for the first banana is:

$$15-1-3 = 11$$

and total consumer surplus:

$$11+10+9+8+7+6+5+4+3+2+1+0 = 66$$

And for the third consumer:

$$p_B^3 = 5-X_E^2/2$$ $$1.5 + 1 + 0.5 + 0 = 3$$

Total consumer surplus becomes:

$$21 + 66 + 3 = 90$$

2.) We have three producers of apples, and they have the following supply curves (marginal cost curves):

$$X_A^{1} = p_A$$ $$X_A^{2} = p_A - 2$$ $$X_A^{3} = 2p_A$$

a.) If the price of apples is 4, how many apples do the three producers make?

b.) What is the total producer surplus?

a.)We input the price into the supply curves:

$$X_A^1 = 4$$ $$X_A^2 = 4-2 = 2$$ $$X_A^3 = 2*4 = 8$$ $$Totalt = 14$$

b.) To calculate the producer surplusses, we need to find the difference between marginal cost and the market price for each producer.

We can rearange our supply curves to get marginal costs:

$$mc_A^1 = X_A$$

The producer surplus for the first apple for producer 1 is:

$$4-1 = 3$$

And for the second:

$$4-2 = 2$$

Total surplus is:

$$3+2+1+0 = 6$$

Marginal cost for the second producer can be written:

$$mc_A^2 = X_A + 2$$

Producer surplus is:

$$1 + 0 = 1$$

Marginal cost for the third producer is::

$$mc_A^3 = 0.5X_A$$

Producer surplus is:

$$3.5 + 3 + 2.5 + 2 + 1.5 + 1 + 0.5 + 0 = 14$$

Total producer surplus is:

$$6+1+14 = 21$$

3.) Assume that a good has a marginal cost of 0 (for example, a digital good like an e-book, where selling one more costs essentially nothing.) What price will maximize the total social surplus?

We maximize the total social surplus by setting the price to 0! The problem then becomes that all of the surplus comes from consumers and then there is no incentive for the producer to make and sell the digital good. While the marginal cost is zero, the producers still have fixed costs that they need to cover.

There are several solutions to this problem. Sometimes, with marginal costs close to zero, the state enters a market in order to supply a good. For example, with some public broadcasting of radio and television.

Another solution is to offer the good as part of an "all-you-can-eat" subscription, like spotify, or to provide the service for free but to sell advertisements.

4.) Let us say that demand for almonds can be written:

$$P=200-X$$

Market supply can be written as:

$$P=50 + 0.5X$$

With a free market, what will consumer and producer surplus be?

We have to calculate the area in the triangles that represent producer and consumer surplus by using the formula for area as: (1/2*b*h)

First, we have to find price and quantity in equilibrium:

$$200-X = 50 + 0.5X$$ $$X^*=100$$ $$P^*=100$$

Using the area formula for a triangle, we can calculate out the consumer surplus:

$$0.5*(200-100)*100 = 5,000$$

And the producer surplus:

$$0.5*(100-50)*100 = 2,500$$