Consider the two social welfare functions WU = U(1) + U(2) (utilitarian)

WR = min{U(1), U(2)} (Rawlsian)

where Ui = ln(Xi

) is the utility enjoyed by the ith generation from the consumption Xi

, i = 1, 2.

Consider two projects:

Project A: Generation 1 reduces consumption by 10 units. The investment yields 20 additional units of consumption for Generation 2.

Project B: Generation 1 reduces consumption by 15 units. The investment yields 15 additional units of consumption for Generation 2.

Let the pre-project level of consumption in Generation 1 be 100 units. Now consider three scenarios:
Scenario Pre-project level of X2 (i) No technology change 100 (ii) Technology improvement 120 (iii) Technology worsening 80 (or loss of inputs)
Use a tick to denote Do project or a cross to denote Do not do project in each cell of the following table to show whether the project (A or B) should be undertaken under each of the three scenarios, for the two cases of a utilitarian SWF (U) and a Rawlsian SWF (R).