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3240Sol assigned questions (Chs2-5).pdf

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ECON 3240
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Solutions to assigned questions Chs25Ch2 Questions 4 and 54 We are given the formula for the marginal rate of substitution of leisure for income or consumption since there is a oneforone tradeoff between the two of themThe MRS is the slope of the indifference curveThe formula that appears is actually the absolute value of the MRS since that expression must be positive Ax must always be positive and C and l must always be nonnegative and the indifference curves have a negative slopea As we move from left to right the amount of leisure increases while Ax remains constant and the value of C fallsThis implies that the value of the MRS decreasesThe interpretation is that as the worker consumes more and more leisure heshe values the marginal hour of leisure less and less and is willing to trade off less and less incomeThe 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 husbands income b Recall that the reservation wage is equal to the slope of the indifference curve at the lower righthand corner solution which corresponds to the situation in which no hours are workedIf h0 the number of hours worked then all of the time endowment T goes to leisureWe can thus writeMRSA x CTwIn order for this woman to participate in the labour market the market wage has to exceed the reservation wage so we can write wAx CTTaking the natural logarithm of both sides of the equation yieldsln wln Axln Cln T Since the logarithmic operation is the inverse of the exponential operation and at the corner solution Cnonlabour income y and we obtain the desired resultThe 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 problemc We treat Z as a random variable which is distributed normallyThat means that it has mean zero and a variance of unityThe graph has a bell shape on a diagram with the probability density of the vertical axis and the values of Z on the horizontal axisAny factor which raises Z makes labour force participation more likelyThe form of that distribution however is not really the focus of this questionAn increase decrease in nonlabour income ln Y would shift the income constraint upward downward making participation less more likelyAn increase decrease in ln W would rotate the income constraint upward downward making participation more less likelyThe impact of the taste shifters depends on whether the sign of the beta coefficient is positive or negativeThey have the effect of changing the slope of the indifference
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