Answer to Question 1
Government failures refer to the broader set of inefficiencies associated with government interventions. The government will sometimes make mistakes, the bureaucracy can be inefficient and slow, and some politicians may be corrupt, seeking to use the process of decision making for their own benefit or their own ideological ends. Taxes and other government activities can distort decisions, leading to deadweight losses. Government failures also include the costs of bureaucracies. Bureaucrats who are employed by the government could have been working in other productive sectors of the economy - this is an important opportunity cost of government work. Large governments also engender the problem of corruption; corruption is the misuse and misallocation of resources by officials in power.
Although there are costs associated with governments and government intervention in the economy, market outcomes are sometimes inequitable, with high levels of inequality and poverty coexisting alongside huge fortunes for a few. Governments use taxation and spending to reduce inequality and poverty in the economy. Markets also fail to take external costs and benefits into account. This gives rise to market failures or externalities. Governments attempt to correct these externalities using command and control strategies and taxes or subsidies. When evaluating government policies, these costs of government have to be considered. How these costs weigh against the benefits of government determine, to a large degree, the extent of government intervention and the optimal size of government.
Answer to Question 2
In a purely competitive labor market the wage rate will eventually equal to the marginal revenue product. The marginal revenue product is equal to the price times the marginal productivity of labor. Therefore, the marginal productivity of labor must be equal to one.
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