Preliminary Information:

Optimizing FAR-FAR = Floor Area Ration

1) P = -F

= Price for all housing and location factors besides FAR

F = FAR

= marginal impact of FAR on Price per square foot.

2). C = + F

= "baseline" cost of "stick" SFU construction

= marginal impact of FAR on cost per square foot

Given:

Profit Function:

Profit Function = P*F - C

Profit Function = F - F2 - ( + F)

Profit Function = F - F2 - - F

Given:

Derivative of the profit function with respect to F (p/F = 0

p/F = - F -

p/F =0

- F - = 0

- = F

F = ( - )/

Question:

Derive optimal FAR or F* ?