eco204_HW_3_solution - 1 s ECO20420082009 AjazHussain...

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1 ECO 204, 2008 2009. Ajaz Hussain. Department of Economics, University of Toronto s ECO 204 2008 2009 Ajaz Hussain HW 3 Solutions Question 1 In lecture 3, we analyzed the effects of a public policy program that gave free education for exactly 12 years of education. Figure 1 depicts the private budget line and public budget point from that question: Figure 1 In this question, you will analyze two variations of that question: (a) “coupons” that can only be used for education (exactly like gift certificates that can be spent only a certain store) and (b) a cash subsidy. Assume consumer has “imperfect substitutes” preferences over education and everything else, which are each good goods.
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2 ECO 204, 2008 2009. Ajaz Hussain. Department of Economics, University of Toronto Note : You may want to read BB p. 114 118 after you attempt this question ‐‐ in their version of this question ‐‐ for housing instead of education ‐‐ they look at the case of someone who consumes less than a “mandated” level of housing. (a) Suppose the government gives everyone a coupon (voucher) which can be used to obtain the up to 12 years of education for free. Analyze the impact of this policy on optimal choice, “happiness” and education levels. Note: in this question, the consumer will have the option of 12 years of education for free and ‐‐ if she wants more than 12 years of education ‐‐ to pay for additional years of schooling. In the lecture question you had to either go to free public schools for 12 years or go to private schooling for any number of years. Answer : The coupon is an education “gift” allowing the recipient to get 12 years of education absolutely free. Let education be on the x axis and everything else on the y axis. The slope of the budget line is: P 1 /P 2 = P education /P else . The coupon makes the first 12 years of education freel; thus, the for the first 12 years, the slope of the budget line is 0. For any education beyond 12 years, the slope will P education /P else . In essence, the budget line shifts out, but leaves the maximum amount of other goods that can be purchased unchanged. The shift is almost as if the consumer has a higher income, except that she cannot spend the extra income on everything else. Figure 2 depicts the initial and new budget constraints: Figure 2 As with the analysis in lecture 3, the impact of the program depends on preferences and initial choices. Three cases are depicted in Figures 3 through 5.
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3 ECO 204, 2008 2009. Ajaz Hussain. Department of Economics, University of Toronto Figure 3 In Figure 3, the consumer avails herself of the voucher program by studying more and buying more of everything else ‐‐ here, everything else and education are normal goods. At the initial and new optimal choice, her MRS = slope of the budget line and she is happier than before.
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