A large apartment complex for low-income renters is being considered. The choice must be made between conventional steel construction and using an innovative scheme of "pushup" construction that promises to cost less. There is uncertainty in the cost estimates in both of the proposals, but clearly it is greater in the case of the latter, untried, system of construction. Assume that the best estimate of the conventional cost is x₀ , with uncertainty in the estimate being summarized by saying there is a 50-50 chance that the true cost will be within x0 ± 0.05x0 . Assume that the best estimate of the pushup cost is 0.8 x₀ , but that the "probable error" is 0.10x0 ; that is, there is a 50-50 chance that the true cost will be within 0.8x0 ± 0.1 x₀ . Assume (for simplicity in your computations) that in both cases the engineer is prepared to state that his uncertainty in the costs can be described by symmetrical triangular distributions, centered on the "best estimates."

(a) As the technical representative of the nonprofit developer, decide which alternative to take if the project is being carried out with funding under government regulations which place a maximum rent on the units and which require that the rent be set so that no profit is made by the developer. The implication to the (charitable) developer is that he will make no money no matter what the construction cost, but he will lose money from his own "pocket" if the construction cost exceeds that value c which the maximum rents (minus interest, etc.) will just cover. This value can be accurately calculated to be c = 1.10 x₀ . Sketch the function of utility to the developer versus the cost.

(b) As the technical representative of an association representing the steel industry, decide whether your industry should underwrite the pushup project by guaranteeing that it will pay any cost in excess of c. Your industry gains nothing if the pushup project is not undertaken, but gains information on a potentially profitable new development, no matter what its final cost. Assume that this benefit to the industry is judged to be worth 0.02 x₀ , independently of the final cost, plus an amount which decreases linearly from 0.05x0 at 40 percent of conventional construction cost to zero at the cost of conventional construction x0 . Sketch the utility to the industry versus true cost.