Power laws (and the special case of Zipf’s law) allow us to characterize cities on a map with a single number, namely the slope of a rank-size curve. These rank-size curves show the rank of a city as a function of its size: the biggest city gets rank 1, the second largest city rank 2, and so on. The slope tells us whether cities are relatively similar in size (small slope) or unevenly sized (steep slope). But what explains the existence of different sized cities? This chapter introduces some urban theories that explain the existence of different sized cities; a graphical representation of the Henderson model and a graphical representation of a state-of-the-art model of differentiated cities as developed by Davis and Dingle.

The electricity grid is the greatest engineering invention of all time. The grid provides light, heat, cold, mechanical power, computation, and communications to billions of people. A key aspect of the grid is that the generators are separated from the consumers by transmission lines. The electricity is generated in favorable locations – hydroelectric dams in the mountains, solar panels in the desert, wind turbines offshore, and coal plants near cooling water. We can see how electricity has grown in importance from Figure 7.1, which shows the electricity share of primary energy over time. It has increased from 9% in 1950 to 41% in 2017. The non-electrical transportation energy share has also grown, but more slowly, from 14% in 1971 to 20% in 2017. These increases came at the expense of non-electrical stationary energy whose share fell from 65% in 1971 to 39% in 2017. The electricity plot has a noticeable curvature.

We introduce three alternative models that extend the core model of Chapter 7. First, the intermediate goods model includes intermediate production and inter-sectoral labour mobility, instead of inter-regional labour mobility. In some cases this leads to a bell-shaped curve instead of the tomahawk diagram, implying that agglomeration gradually rises and falls as transport costs decline. Second, the generalized model incorporates both the core model and the intermediate goods model in one framework. Third, the solvable model introduces a second production factor (such as human capital) in the manufacturing sector. This model leads to explicit solutions for factor rewards. We conclude with an empirical evaluation of urban power laws and show that adding congestion to the core model allows us to better understand the influence of parameter changes on estimated power law exponents.

For almost all of human history and for almost all people, the most important question each day has been, “Will our family have enough food to eat?” That, is until the Green Revolution. In the 1950s American agronomist Norman Borlaug (Figure 6.1), funded by the Rockefeller Foundation, developed a hybrid that was a cross between a Mexican wheat that was well adapted to a range of conditions and a short, stiff Japanese wheat that could support the weight of extra grains. This allowed farmers to apply more fertilizer without the wheat lodging, that is, falling over. Mexican farmers began growing Borlaug’s dwarf wheats in 1961 and doubled their yield. Since then there has been a spectacular increase in world crop yields. Figure 1.21 showed the history for cereals. Borlaug also argued that increasing crop yield was the best way to reduce deforestation. This has been called the Borlaug hypothesis. We will see in Section 6.5.1 that there is evidence to support his idea.

The resources of oil, gas, and coal are finite. The time will come when their production will fall, never to rise again. Alternatives are our once and future energy supply. So what did people do before fossil fuels? Many of their needs were similar to ours. People required light at night. They wanted to travel and to ship their goods. Farmers needed help plowing their fields. At high latitudes, people must have heat to survive. We will discuss three of their energy sources: horses, whale oil, and wood. Horses carried riders and they pulled plows, like tractors today. Whale oil provided light and wood produced heat. We conclude the chapter with a look at a society with a limited energy supply – the Norse Greenland colony.

Stationary demand is the energy that is not used for transportation. It includes homes, offices, factories, mines, and farms. Stationary demand was 77% of total primary energy demand in 2017, so it is much larger than transportation demand. The share has been stable; it was also 77% in 2000. Figure 8.1 shows the history of world stationary demand. The character of demand differs from supply. Much of demand comes from families and small companies, while energy suppliers are typically large companies. For this reason, we will be plotting demand on a per-person basis. Demand data are not as good as supply data. The demand data series do not go back far in time and there are gaps. Lights, heaters, refrigerators, and air conditioners have had significant efficiency improvements in recent years, but changes in stationary demand are not dramatic. There is nothing in the history of stationary demand comparable in scale to the fracking revolution or the explosive growth of solar PV.