Building on the general equilibrium setup solved in the last week, this lecture looks in depth at the relationships between productivity, patience, prices, allocations, and nominal and real interest rates. The solutions are given to three of Fisher's famous examples: What happens to interest rates when people become more or less patient? What happens when they expect to receive windfall riches sometime in the future? And, what happens when wealth in an economy is redistributed from the poor to the rich?

Philosophers and theologians have railed against interest for thousands of years. But that is because they didn't understand what causes interest. Irving Fisher built a model of financial equilibrium on top of general equilibrium (GE) by introducing time and assets into the GE model. He saw that trade between apples today and apples next year is completely analogous to trade between apples and oranges today.

Over time, economists' justifications for why free markets are a good thing have changed. In the first few classes, we saw how under some conditions, the competitive allocation maximizes the sum of agents' utilities. When it was found that this property didn't hold generally, the idea of Pareto efficiency was developed. This class reviews two proofs that equilibrium is Pareto efficient, looking at the arguments of economists Edgeworth and Arrow-Debreu.

Our understanding of the economy will be more tangible and vivid if we can in principle explain all the economic decisions of every agent in the economy. This lecture demonstrates, with two examples, how the theory lets us calculate equilibrium prices and allocations in a simple economy, either by hand or using a computer. In future lectures we shall extend this method so as to compute equilibrium in financial economies with stocks and bonds and other financial assets.

This lecture explains what an economic model is, and why it allows for counterfactual reasoning and often yields paradoxical conclusions. Typically, equilibrium is defined as the solution to a system of simultaneous equations. The most important economic model is that of supply and demand in one market, which was understood to some extent by the ancient Greeks and even by Shakespeare. That model accurately fits the experiment from the last class, as well as many other markets, such as the Paris Bourse, online trading, the commodities pit, and a host of others.

This lecture gives a brief history of the young field of financial theory, which began in business schools quite separate from economics, and of my growing interest in the field and in Wall Street. A cornerstone of standard financial theory is the efficient markets hypothesis, but that has been discredited by the financial crisis of 2007-09. This lecture describes the kinds of questions standard financial theory nevertheless answers well. It also introduces the leverage cycle as a critique of standard financial theory and as an explanation of the crisis.

The final exam was administered in class.

In this final lecture, Professor Saltzman talks about artificial organs, with a stress on synthetic biomaterials. First, the body's responses (immunological and scar healing responses) to foreign materials are introduced. This leads to discussion of different types of polymer/plastic materials (i.e., Dacron and GORE-TEX) and their properties. Next, Professor Saltzman talks about the design and function of some artificial organs, such as lens implants, heart valves and vessels, hip, dialyzer, heart/lung bypass machine, and the artificial heart.

Professor Saltzman uses cancer diagnosis and treatment as an example to demonstrate the some applications of biomedical engineering technologies and methods. Some issues involved in cancer treatment, such as tumor angiogenesis, radiation sensitivity, drug localization, and cancer stem cells are mentioned. Next, he describes the phases (I-IV), in compliance to guidelines enforced by the Food and Drug Administration (FDA), which a new drug compound must go through to gain approval prior to public distribution/sale.

In this lecture, Professor Saltzman continues his discussion of tissue engineering, and its role in facilitating healing, tissue regeneration, organ replacement, drug delivery and as model for studying human physiology. Specific examples from current research by scientists at Yale are used to illustrate some of these points and to highlight the current progress in the field. Some examples are generating neo-tissues from hydrogel scaffold seeded with cells, healing spinal cords and controlling mechanical properties of newly grown blood vessels with external conditions.