In chapter 28, Mankiw focuses on the natural rate of unemployment (a long-run problem). Unemployment is important because it decreases from the economy's GDP, and thus the economy's standard of living. Unemployment is an imperfect measurement from the BLS of those who want to work but who do not have jobs, perhaps because of either frictional or structural unemployment. For example, discouraged workers (individuals who would like to work but have given up looking for a job) are not included in the measurement.
I am a little confused about the "seemingly contradictory" result: most spells of unemployment are short, and most unemployment observed at any given time is long-term; and the example of the four government employment workers did not help.
It is important to note that the unemployment is never zero, but fluctuates around the natural rate of unemployment. This is due to frictional unemployment (it takes time for workers to search for the jobs that best suit their tastes and skills) and structural unemployment (unemployment that results because not enough job positions).

Chapter 27: The Basic Tools of Finance

Chapter 27 discusses finance, or the field that studies how people make decisions regarding the allocation of resources over time and the handling of risk. We were given the equation to find future value (assuming the account was being compounded), which is FV=(1+r)^y * PV. To get present value, one would just divide. The chapter then discussed managing risk in regards to risk aversion (those whose pain of loss exceeds pleasure of winning), the markets for insurance (where the goal is to spread risks around more efficiently, but it faces adverse selection and moral hazard), diversification of firm-specific risk (reducing risk by replacing a single risk with a large number of smaller, unrelated risks), and the trade-off between risk and return (stocks offer higher potential risk and return).
The standard deviation part confused me a bit. I know a variable typically stays within two standard deviations of its average about 95 percent of time, but I just remember this as a fact. I haven't really applied it to anything, so I was confused when the book said,"thus, while actual returns are centered around 8 percent, they typically vary from a gain of 48 percent to a loss of 32 percent." Otherwise, the chapter was fine but I want to go over the math.

Article Review

David Stockman discusses the December "job" report, stating that it is the last positive delta standing. However, it is only positive because of fake numbers; basically, it's BS from the BLS. Numbers are over inflated using "seasonal adjustment". Therefore, the job report does not reflect the actual state of the economy, which is "knocking at the door of a recession." The number is used by pretentious wall streeters wearing fake smiles, who want buyers to keep on buying (where stock market prices are also probably a lie too).
The job report does not take into consideration different types of jobs or salary distribution. It counts jobs that are "born again", after being lost from-you guessed it-the crashes/collateral damage of the financial bubble crash. The report is rubbish.
Though a little hard to understand, it is evident that no matter what pointless "facts" are thrown in our face, we need to fear and expect a recession; a recession that has been prolonged and denied for as long as possible by people like Ben Bernanke (who, before a crash, called the economy "the great moderation". Ha.)
I appreciate Stockman's passionately honest tone, as he is someone that will not put up with lies/deceit. The article, though not containing pleasant information, was a good read.

Chapter 26: Saving, Investment, and the Financial System

Mankiw introduces saving, investment, and the financial system in chapter 26. The financial system the group of institutions in the economy that help to match one person's saving with another person's investment; this is special characteristic of financial markets because they link current income with future purchasing power. The categories of financial institutions in the U.S. are financial markets (bond and stock markets) and financial intermediaries (banks and mutual funds).
The difference between a financial market and financial intermediary is that a financial market is an institution through which savers can directly provide funds to borrowers, whereas a financial intermediary is more indirect.

There was a lot of information in this chapter, and I thought it was kind of a weird transition from GDP + CPI (which were more closely related). However, I think the chapter did a good job emphasizing the importance of financial systems, which made the chapter more interesting. 

Chapter 24: Measuring the Cost of Living

The cost of living over time is measured by the consumer price index, which is a measure of the overall cost of the goods and services bought by a typical consumer. This CPI is measured monthly by the Bureau of Labor Statistics in these five steps: fixing the basket (determining which prices are most important to the typical consumer), finding the prices of the goods in the basket, computing the basket's cost (the prices change, but the quantity does not), choosing a base year and computing the index, and computing the inflation rate.
This calculation is used for specific metropolitan areas within the country, some narrow categories of goods and services, and calculating the producer price index, which can be used to predict changes in the consumer price index.
The problems with CPI are the substitution bias, the introduction of new goods, and unmeasured quality change.
The GDP deflator and CPI are different in that the GDP deflator reflects the price of all goods and service produced domestically, whereas the CPI reflects the prices of all goods and services bought by consumers (including foreign goods). Also, CPI has a fixes basket of goods compared to GDP that compares the price of currently produced goods and services.

Chapter 23: Measuring a Nation's Income

This chapter discussed one of the basics of macroeconomics: GDP (gross domestic product), or the market value of all final goods and services produced within a country in a given period of time. GDP measures the total income of everyone in the economy and the total expenditure of the economy's output of goods and services; where for an economy as a whole, income must equal expenditure due to the interactions of two parties: the buyers and sellers. The identity for GDP is Y=C+I+G+NX, and the GDP is typically calculated in time periods of a year or quarter (*the quarter rate usually presents GDP at an annual rate*).
Though this chapter went in depth about GDP, it threw a lot of vocabulary words at the reader and did not expand on ones that I felt needed more clarification. The FYI, which will be on the AP test, was very vague. Terms mentioned were GNP (total income earned by a nationals even if abroad), NNP (the total income of a nations's residents minus depreciation), National Income (total income earned by a nation's residents; excluding indirect business taxes and business subsidies), Personal Income (income that households and non corporate businesses receive; excluding retained earnings, subtracts corporate income taxes+contributions for social security, and includes interest and transfer program incomes), Disposable Personal Income (=Personal Income-(personal taxes+certain non tax payments)).
The chapter then went on to discuss the four components of GDP: consumption (C), investment (Y), government purchases (G), and net exports (NX), real versus nominal GDP, GDP Deflators, and the pros/cons of using GDP to measure economic well-being.