Answer to Question 1
Household income changes over the life cycle of the household, which leads to an overestimation of inequality among households. At young ages, income is relatively low, peaks in middle ages, and then falls after retirement. The standard measures of income distribution do not account for age differences among households. They, therefore, overestimate the inequality because the distribution of lifetime income is more equal than the distribution of annual income.
Answer to Question 2
The marginal rate of substitution is the rate at which a person will give up the good measured along the y-axis in order to get more of the good measured along the x-axis. The marginal rate of substitution equals the magnitude of the slope of the indifference curve. Because the indifference curve is not linear, the marginal rate of substitution changes as the consumer moves along the indifference curve. In particular, as more of the good measured along the x-axis is consumed, its marginal rate of substitution diminishes. In general, as more of a good is consumed, its marginal rate of substitution decreases.
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Solow Model with Saving Dependent on Income Level
To satisfy the inequality, sketch the following function by hand and shade the graph regions.