A firm, existing for two periods, produces output using capital and labour. The firm's production at any time i can be described by a simple production function f(k.-, m}. The firm faces the foilmving profit function expressed in real terms: file. \"2) + k2 + (e + 12131 \"an: f.\"1]+k1ka+(51+d1]3o5131W191+ 1+r a,-, s.- and d.- denote the quantity and price of shares as well as dividend payments of shares held by the firm in period i in real terms. The firm has to borrow to invest in new capital stock. The amount it can borrow is constrained by the value of its stock holdings: [kg k1) 2 H5131 where Fr' 1:: 1 is a parameter that limits investment spending to a fraction of the firm's stock holdings. {a} Set up the constrained optimisation problem and derive the first-order con- ditions for :11. n2. k: and al. {5 marks) (b) Using the first-order conditions for it? and a1. show that a binding borrowing constraint will reduce the capital stock in the second period. {14 marks} {c} Assume that the economy is hit by a shock that reduces the second period real share price, 52. in your own words, describe the nancial accelerator mechanism that can be triggered by such a deciine in asset prices. [14 marks]