Brad DeLong posts two criticisms of Piketty's book. One is a predictable criticism from the conservative National Review. Piketty's research is about a fundamental contradiction in capitalism His book is about the consequences of that contradiction. That is, inequality is built into capitalism because the return on capital, which is highly concentrated, grows faster than the economy and national income. Since Karl Marx also wrote about a fundamental contradiction in capitalism, Piketty must be a Marxist, and therefore he must be wrong about capitalism. This cannot be a serious criticism for a couple of reasons. In the first place, Piketty was trying to explain something very real. That is, there is a long history of income inequality in capitalism. His book has received a lot of attention because it contains a lot of historical data which attempts to explain an important historical relationship between the return on capital and the growth of the economy. Piketty's solution to the problem of income inequality is to use the tax system to redistribute income. He does not argue for overthrowing the system of private property. Therefore, he has been criticized by Marxists for making an effort to maintain the system of private property.
The second critique of Piketty comes from an economist who shares many of the concerns that Piketty has about growing income inequality and the concentration of wealth. In fact, he has written extensively about that problem and he has developed his own methods for measuring income inequality. His critique is primarily about Piketty's definition of capital. His argument is that Piketty does not distinguish between productive capital and other assets. He thinks that the title of Piketty's book should be Wealth In The 21st Century.
The comments following DeLong's post are worth reading. Most, if not all of the comments, are about the distinction between capital and wealth. The first criticism was ignored but it will probably be the most frequently used tactic against Piketty's explanation of the relationship between income inequality and capitalism. Its a lot easier to dismiss Piketty as a Marxist than it is to attack his explanation for income inequality.