3240sol1 - Solutions to assigned questions (Chs2-5). Ch2:...

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Solutions to assigned questions (Chs2-5). Ch2: Questions 4 and 5 4. We are given the formula for the marginal rate of substitution of leisure for income (or consumption, since there is a one-for-one trade-off between the two of them). The MRS is the slope of the indifference curve. The formula that appears is actually the absolute value of the MRS, since that expression must be positive (A(x) must always be positive, and C and l must always be non-negative), and the indifference curves have a negative slope. a) As we move from left to right, the amount of leisure increases, while A(x) remains constant, and the value of C falls. This implies that the value of the MRS decreases. The interpretation is that as the worker consumes more and more leisure, he/she values the marginal hour of leisure less and less, and is willing to trade off less and less income. The variables (labelled X) which might affect the MRS are the number of children that the woman has, as well as their ages, her level of education, and her marital status (tied with her husband’s income). b) Recall that the reservation wage is equal to the slope of the indifference curve at the lower right-hand corner solution, which corresponds to the situation in which no hours are worked. If h = 0, the number of hours worked, then all of the time endowment T goes to leisure. We can thus write: MRS = A (x) C / T = w*. In order for this woman to participate in the labour market, the market wage has to exceed the reservation wage, so we can write: w > A(x) C / T. Taking the natural logarithm of both sides of the equation yields: ln w > ln (A(x)) + ln C - ln T. Since the logarithmic operation is the inverse of the exponential operation, and at the corner solution, C = non-labour income (y), and we obtain the desired result. The log of the time endowment T can probably be interpreted as a constant across almost all women, and so it can probably be ignored at this stage of the problem. c) We treat Z as a random variable which is distributed normally. That means that it has mean zero and a variance of unity. The graph has a bell shape on a diagram with the probability density of the vertical axis and the values of Z on the horizontal axis. Any factor which raises Z makes labour force participation more likely. The form of that distribution, however, is not really the focus of this question. An increase (decrease) in non-labour income ln Y would shift the income constraint upward (downward), making participation less (more) likely. An increase (decrease) in ln W would rotate the income constraint upward (downward), making participation more (less) likely. The impact of the taste shifters depends on whether the sign of the beta coefficient is positive or negative. They have the effect of changing the slope of the indifference
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curve. 5.
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This note was uploaded on 02/05/2011 for the course ECON 3610 taught by Professor Steve during the Fall '11 term at York University.

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3240sol1 - Solutions to assigned questions (Chs2-5). Ch2:...

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