Wage safety trade off model

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Week 9
Exercises:
1. Wage safety trade off model:
Utility function: U=WS
Iso
profit function: W+S 2 = 100
a. If the optimal level of S is 5.77, determine the utility maximum level of W and S and compute the level of utility at that level.
b. Show the optimal level graphically.
c. Now suppose because of the government regulation, the safety level should be at least 7. Compute the wage rate and the level of utility. Is the individual better off with this policy?
2. Now utility is U= WS and the iso profit is W 2 +S=
a. If the optimal level of S is 66.59, determine the utility maximum level of W and S and compute the level of utility at that level.
b. Show the optimal level graphically.
c. Now suppose because of the government regulation, the safety level should be at least 75. Compute the wage rate and the level of utility. Is the individual better off with this policy?
3. Suppose that building the oil pipeline across Alberta required the use of many construction workers recruited from the continental Canada who lived in dormitories and worked in an inhospitable climate. Discuss the creation of a compensating wage differential for these jobs.
4. For underwater construction workers, Wi = 10 + 0.5D, where w = wage in dollars per hour and D = the depth underwater at which workers work, in meters. Based on this information:
a. Draw the offer curve.
b. Suppose Worker A works at a depth of 3 meters and Worker B works at a depth of 5 meters. Draw the possible indifference curves for each worker.
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c. At their current wages and depths, what is the trade-off between hourly wages and a 1-meter change in depth that each worker is willing to make?
d. Which worker has a greater willingness to pay for reduced depth at 3 meters of depth?
5. Suppose that the utility and isoprofit functions are given as:
𝑊=𝑈+𝑅2,𝑊=10+ 12 √𝑅
a. If the optimal level of R is 0.25, determine the utility maximum level of W and compute the level of utility at that level.
b. Show the optimal level graphically.
6. Chapter 8 Review Question #1, Problems #1, 6, 7, and 8.
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