Draw the indifference curve for someone deciding how to allocate time between work and leisure. Suppose the wage increases. Is it possible that the person's consumption would fall? Is this plausible? Discuss. (Hint: Think about income and substitution effects.)

Understanding the income and substitution effects is essential for analyzing how individuals alter their labor and leisure choices in response to wage changes. Let's start by breaking these effects down.

The substitution effect occurs when a wage increase makes working hours relatively more valuable compared to leisure time. As a result, the individual is incentivized to work more and enjoy less leisure to take advantage of the higher wage rate. It's as if work 'buys' more than leisure now, so the individual 'purchases' more working hours.

In contrast, the income effect arises because the wage increase effectively boosts the individual's purchasing power. They can now afford to maintain their original level of income while indulging in more leisure time. This effect may prompt them to 'buy back' some leisure time, decreasing their hours of work. The overall change in labor supply will depend on which of these effects is stronger.

A budget constraint represents the trade-off between different choices given limited resources. In the case of labor and leisure, the 'resource' is time, and the individual must decide how to allocate their finite hours.

The constraint is shown graphically by a line on a graph with axes representing leisure time and income. It slopes downward, highlighting the trade-off: increasing leisure slices into work time and therefore income. When wages rise, the budget constraint pivots outward, allowing the individual to achieve higher levels of income for the same amount of labor or maintain their income with fewer hours worked. This change in the budget line is what triggers the income and substitution effects.

The decision between labor and leisure can be thought of as a balance scale, where on one side you have the joy and relaxation of leisure, and on the other, the financial benefits of labor.

Economists use the concept of opportunity cost to analyze this trade-off. Each hour of leisure costs the individual what they could have earned by working. When wages increase, the opportunity cost of leisure goes up, making work financially more appealing. However, personal preferences play a crucial role and might lead some individuals to value leisure over the additional income they could earn. It’s a dynamic balancing act that can sway differently for each person depending on their circumstances and preferences.

The effect of a wage increase on labor supply is a subject of considerable interest in economics. As wages rise, we might intuitively expect people to work more to earn more. However, it's not that straightforward.

Here's a crucial point: if the substitution effect dominates, then the labor supply increases — workers will want to take advantage of the higher wage rate. Conversely, if the income effect is stronger, labor supply might decrease as individuals opt for more leisure, now that they can afford their desired lifestyle with less work.

Utility maximization is the goal behind the decisions of how much labor and leisure to enjoy. It refers to the choice combination that gives the highest level of satisfaction to the individual given their income and the market wages.

An indifference curve graphically represents this behavior, as it combines various quantities of labor and leisure that yield the same utility to the individual. The point where the budget line is tangent to the highest possible indifference curve is where utility is maximized. In response to a wage increase, the individual will align their labor and leisure mix to the new budget constraint to find a new point of utility maximization, which might be more leisure-heavy if the income effect overshadows the substitution effect.