p.p1 low wage. Then, due to the substitution effect

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For example, if the worker was offered an increment of his wage from $20 to $40 an hour. The wage increase would tilt the budget line right from the endowment point (as illustrated in figure 1). This shift of the budget line changes the opportunity set from AE to BE. However, the endowment point (point E) remains the same as the amount one consumes when one is not working is constant, irrelevant to the value of the wage. This shift of the budget line provides a larger opportunity set (more indifference curves) for the worker and causes the worker to move to a higher indifference curve, moving from point C to F due to the income effect (the effect on demand when there’s a change in real disposable income), increasing hours of work by 5. This is because the higher wages will cause the worker to work more hours in order to reach the desired income as he is on a relatively low wage. Then, due to the substitution effect (the effect on demand when the value of the good changes, given that income is constant), as work becomes relatively more profitable than leisure, the worker will be incentivised to move along the indifference curves from point F to G, increasing hours of work by 15 hours. Therefore, due to the worker’s relatively low wage, the substitution effect would dominate the income effect (people on low wages are more responsive to higher wages) and the wage increase would move the worker to a higher indifference curve and shift the optimal consumption point from point C to point G, overall increasing hours of work to 80 hours. Thus, in this case, the statement holds true as the worker has increased his work hours to 80 hours and reduced his leisure hours to 25 hours. 

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However, if the worker had different characteristics such as laziness and preferred leisure over work. His individual labor supply curve would be more inelastic (a change to the wages would cause an even smaller change in hours worked) in which case, the negative income effect would dominate the substitution effect. The worker has already reached his desired income, and hence, will not be incentivised to work more if the hourly wage increases. He may even reduce his work hours as he’ll be able to earn the same as he had before in fewer hours and can, in turn, spend more time for leisure. Hence, this statement is not always true. It is dependent on a variety factors including the worker’s preferences, characteristics, and current income. Likewise, in both cases, there is an assumption that the worker has the ability to change the working hours. In reality, not every worker possesses flexible working hours. Some would have fixed hours which means that the worker would not be able to change their working hours regardless of whether wage rates have changed. Thus, the correctness of the statement varies depending on every scenario.