John is the Southwestern Regional Manager for the National Forest Service and has to make decisions about how many rangers (R) to hire and how many new trails (T) to cut for recreational use. John’s budget for Tonto National Forest in 2018 is $400,000. The cost of hiring a ranger for the season is $50,000, while the cost of cutting a new trail is $80,000 (note, these figures are completely made up).
(a) Write John’s budget constraint and graph the budget set, placing trails on the y axis. Note: be careful to label your axes and intercepts.
(b) What is the slope of the budget line?
(c) T/F: John can afford to hire 4 rangers and build 3 new trails in 2018. Explain using math and/or graphical illustration. 1
(d) Suppose John’s current plan is to hire 3 rangers and cut 2 new trails in 2018. The marginal utility of the third ranger is 543,750. The marginal utility of the 2nd trail is 725,000. John has some room left over in his budget. If he is trying to maximize his utility, should he hire another ranger or cut another trail? Explain.