Problem 1. You have two midterm exams coming up and have to decide how to allocate your study time. After eating, sleeping, exercising, and maintaining some human contact, you still have 15 hours each day to study for your exams!! You have figured out that your GPA (G) from your two courses, economics and sociology, takes the form 1 = ÷(2ve+ vs) 8. where e is the number of hours per day spent studying economics and s is the number of hours per day spent studying sociology. You only care about your GPA. (a) What is your optimal allocation of study time? (b) If you follow this strategy, what will your GPA be? (c) What is the shadow value, measured in GPA units, of the study time? Discuss. [Hint: The optimal value of the Lagrange multiplier is the shadow value of the constraint.]
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- Scenario The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low-income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 10kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnecessarily paternalistic; depriving low-income households of the choice of how to spend their income. These groups argue that the government’s…Scenario The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low-income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 10kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnecessarily paternalistic; depriving low-income households of the choice of how to spend their income. These groups argue that the government’s…Scenario The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low-income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 10kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnecessarily paternalistic; depriving low-income households of the choice of how to spend their income. These groups argue that the government’s…
- Scenario The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low-income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 10kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnecessarily paternalistic; depriving low-income households of the choice of how to spend their income. These groups argue that the government’s…Scenario The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low-income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 10kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnecessarily paternalistic; depriving low-income households of the choice of how to spend their income. These groups argue that the government’s…Scenario The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low-income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 10kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnecessarily paternalistic; depriving low-income households of the choice of how to spend their income. These groups argue that the government’s…
- Scenario The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 10kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnec- essarily paternalistic; depriving low income households of the choice of how to spend their income. These groups argue that the government’s…Scenario:The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 5kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 5kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnec- essarily paternalistic; depriving low income households of the choice of how to spend their income. These groups argue that the government’s…Ten years ago, the town of Easton decided to increase its annual spending on education so that its high school graduates would be able to earn higher wages. Now Easton has asked you to evaluate the effectiveness of the spending increase. Their data show that before the spending increase, the average annual salary of recent high school graduates was $25,000 and that now that average salary has risen to $28,500. Fortunately for your analysis, a neighboring community (Allentown) did not change its annual spending on education. Ten years ago, recent Allentown high school graduates earned an average of $22,500, and now that average is $23,750. (a) Use a difference-in-differences estimator to determine whether Easton’s spending increase caused the wages of their high school graduates to increase. (b) What underlying assumption do you have to make in order for your estimate to be valid? What might cause your underlying assumption to be invalid? (c) This data set contains only two…
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