Perloff Econ 100A 2003 Midterm 1 Solutions A1. A. The original budget constraint L is a downward sloping straight line with a slope equal to the price of child-care. Optimum point e1 is a point where L is tangent to the best attainable poor parents’ indifference curve I1. When Congress gives poor parents a price subsidy, effective price of child-care to parents falls, and the budget constraint rotates outward to LPS so that the slope of the new budget is flatter (because of lower price of child-care), as shown in the diagram. The new optimum point e2 is a point of tangency between LPS and the new indifference curve I2 corresponding to a higher utility level. If child-care is a normal good for poor parents, the income and substitution effects both work in the same direction, and consumption of child-care unambiguously increases while consumption of all other goods may either increase or decrease depending on the parents’ tastes. If child-care is an inferior good, the two effects (at least) partially offset each other. The total effect on consumption of child-care is uncertain. All other goods, $ I2 I1 e1 e2 LPS Child care, units LB. The new lump-sum subsidy is just an increase in the budget given the same relative prices as in case of initial budget constraint L. Therefore, LLS is a parallel shift of L. Then we know that the lump-sum subsidy can buy poor parents the same bundle as a price subsidy. This means that LLS should pass through point e2. The new optimum point e3 should be somewhere on LLS between e2 and the other point where LLS crosses I2. Optimum e3 belongs to an indifference curve I3, which corresponds to higher utility than I2.LLS All other goods, $ I1 e3 e1 e2 I3 I2 LPS LChild care, units C. The recipients should prefer the lump-sum subsidy as it would put him/her on a higher indifference curve thereby giving him/her more utility. (Refer to part A & B) In addition, the lump-sum subsidy would provide him/her with the freedom to consume a larger mixture of options. (1 point given if student only mentioned this point). D. The price subsidy would result in poor parents purchasing more childcare services. This is obvious from the construction of curves in part A & B). The intuitive reason behind this is that parents are given money to be spent on childcare only, therefore automatically increasing the consumption of childcare. The lump-sum subsidy however, could be invested in other goods than childcare. Note that this price subsidy does not lead to only an increase in purchase of childcare services. It can also lead to increase in consumption of other goods as some of the budget that was previously allocated to childcare services is now freed to be invested in other goods. This amount however cannot be greater than the total amount of subsidy.B1. r S(r)+T S(r) reqm r D(r) Qs1 Qs0 Qeqm Qd Quantity of Loans Effects of binding usury law: ● The interest rate in the market falls by (reqm – r). ● The quantity of loans in the market falls by (Qeqm - Qs0). ● There is an excess demand given by (Qd - Qs0) after the law is imposed. Effects of a specific tax given the existence of a binding usury law: ● The interest rate in the market remains r. ● The quantity of loans in the market falls by (Qs0 - Q s1 ). ● There is an excess demand given by (Qd - Qs1) > (Qd - Qs0). ● Suppliers bear the entire incidence of the tax. B2. Jeannie maximizes her utility by consuming at an allocation on her budget line for which the slope of the indifference curve equals the slope of her budget line. This point is found by using the last dollar rule:)1(25125XZXZPMUPMUZZXX=== Another way of deriving (1) is to directly set MRS = MRT: XZMUMUMRSZX−=−= and 25125−=−=−=ZXPPMRT so we have 25=XZ or . XZ 25=Jeannie gets a second equation from the fact that the allocation must be on her budget constraint so ZPXPYZX+= or .25600 ZX+= (2) Substituting (1) into (2) yields: 1225300253002)(600=====+=ZXZZZZ Jeannie’s utility is maximized by consuming {X=12,Z=300}. Note: There are a few other, equally valid ways to solve this problem, e.g. Lagrange Multiplier, substituting the constraint into the utility function. B3. I. The appropriate graph is a labor-leisure diagram, with the budget line kinked at 16 hours, as Larry may only work 8 hours at his first job. The indifference curve should be tangent to the budget line at a time of 12 hours, as Larry works four hours at his second job.II. $1 of goods e1 Slope=-w2 IC1 Slope=-w1 L1121624Hours of Leisure $1 of goods IC2 IC1 L2121624Hours of Leisure Above is a possible outcome when Larry is allowed to work as much as he wants at wage w1. The way the indifference curve is drawn, Larry works about the same amount of hours as he did when his hour were restricted. This is not necessary. The number of hours that he works could go up or down. Clearly, he would only want to work at his high wage job. For full credit, you had to mention that his hours worked could increase or decrease depending on the shape of his particular indifference curves.III. Intuitively, it would seem unreasonable for Larry to work exactly 8 hours when his hours e ith well-behaved indifference curves (which we always assume, unless otherwise stated), it an , it Larry worked 8 hours, the slope of his new indifference curve must be –w1 at 8 hours of work n) –1. 7 Points he Marginal Physical Product of Labor is given by the partial derivative of output with respect are unrestricted. If the lower wage could make him work more, then a higher wage should makhim work more as well. Graphically, $1 of goods urs of ure 241612 IC1 IC*2 L2Ho LeisWwould be impossible for Larry to work exactly 8 hours. In fact, he would have to work more th8 hours. A full-credit answer would have to deal with the shape/slope of the indifferent curves. It was not enough to say that such an indifference curve would cross the original onemust be shown as follows: If(in order to achieve tangency). The slope of the old indifference curve, IC1, must be greater than (less negative than) –w2 at 8 hours of work by convexity of the indifference curves. When coupled with the convexity of IC*2, which confines
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