Suppose Mona and Tom are the only citizens in Winterland and their utility functions are presented by the following equations Um 0 5 ln Xm 0 5 ln Pm Ut 0 5 ln Xt 0 5 ln Pt where X represents consumer goods and services and P pollution and ln the natural logarithm Assume Xm Xt 50 and Pm Pt 25 What are the marginal utilities of X and P for Mona and Tom Assume the Social Welfare Function (SWF) is an unweighted sum of individual utilities Write the SWF and calculate its value Assume Mona is rich, but Tom is impoverished We take 5 units of X from Mona and give it to Tom and as a result of that Pmgoes down to 20 and Ptincreases to 30 How will SWF change Show your calculations Now assume that the Tom's utility function changes as follows Ut 0 8ln Xt 0 2 ln Pt Calculate SWF given the allocation of X and P in (3) 5 Assume Mona lives now, but Tom is not yet born Use the original utility functions, but assume Mona's consumption increases to 80 generating 25 units of pollution today and 30 units in future for Tom Also, as a result of Mona's excessive consumption, Tom's consumption will decrease to 20 Calculate the value of the SWF 6 Now assign a weight of 2 to Tom's utility function in the SWF Recalculate the SWF with the allocations in (5) and compare the results What type of environmental standard does this SWF represent

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Suppose Mona and Tom are the only citizens in Winterland and their utility functions are presented by the following equations: Um= 0.5 ln Xm- 0.5

Suppose Mona and Tom are the only citizens in Winterland and their utility functions are presented by the following equations:

Um= 0.5 ln Xm- 0.5 ln Pm

Ut= 0.5 ln Xt- 0.5 ln Pt

where X represents consumer goods and services and P pollution and ln the natural logarithm. Assume Xm= Xt=50 and Pm= Pt= 25.

What are the marginal utilities of X and P for Mona and Tom?
Assume the Social Welfare Function (SWF) is an unweighted sum of individual utilities. Write the SWF and calculate its value.
Assume Mona is rich, but Tom is impoverished. We take 5 units of X from Mona and give it to Tom and as a result of that Pmgoes down to 20 and Ptincreases to 30. How will SWF change? Show your calculations.
Now assume that the Tom's utility function changes as follows:

Ut= 0.8ln Xt- 0.2 ln Pt

Calculate SWF given the allocation of X and P in (3).

5. Assume Mona lives now, but Tom is not yet born. Use the original utility functions, but assume Mona's consumption increases to 80 generating 25 units of pollution today and 30 units in future for Tom. Also, as a result of Mona's excessive consumption, Tom's consumption will decrease to 20. Calculate the value of the SWF.

6. Now assign a weight of 2 to Tom's utility function in the SWF. Recalculate the SWF with the allocations in (5) and compare the results. What type of environmental standard does this SWF represent?