Solve the following questions showing all the relevant working.

You are given the following data relating to an economy: Ca = 0.7Y I = $33m G =$12m X = $15m (i) Calculate the equilibrium level of national income. [1] (ii) If the national income were (250 million, calculate the unplanned change in stock levels. [1] (iii) Calculate the change in national income if planned investment rises from $33 million to f42 million. [1] [Total 3]Consider the following equations relating to a multiple decrement table with three decrements o, / and y : (ap), = (1-q, )(1-q2 )(1-q;) II (aq), = (ap)" up, di 0 III log(ad) d.x Which of these equations are necessarily correct, assuming that all the functions are differentiable, and that (au)" = up? [3]