. The real intertemporal model with investment. Based on the model discussed in class and Williamson (2014), determine if the following propositions are true or false. If true, prove it math- ematically or graphically (including a brief explanation). If false, provide a counterexample or a rigorous argument. (a) Suppose that G = T . An increase in future total factor productivity stimulates private saving (SP > 0). (b) A negative oil shock understood as a temporary fall in TFP causes a recession (Y < 0) and lower employment (N < 0) . (c) A natural disaster that destroys part of current stock of capital reduces current output but stimulates current investment. (d) Assume that a firm that borrows will borrow at the real interest rate: rl = r + x, where x is the default premium. A rise in the default premium has an ambiguous effect on current consumption.