. Kindly solve the following problems.

12. Consider a small open economy with fixed prices and wages. Consumption depends positively on disposable income, investment depends neg atively on the domestic interest rate, and net exports depend negatively on income and negatively on the nominal exchange rate (defined as the foreign-currency price of domestic currency) Suppose the government has persistently run a large budget deficit D = G - T, which has led to worries about the government defaulting on its bonds. There is perfect capital mobility, but because of fears of default, investors are willing to hold domestic bonds only if the interest rate / exceeds the foreign interest rate i" by a positive risk premium s. Balance-of-payments equilibrium therefore requires i = i' + s, which means the BP line in the IS-LM-BP diagram is horizontal at i* + s. The economy begins in internal (IS-LM) and external (BP) equilibrium running a current account deficit. Assume the government has a fixed exchange rate policy and adjusts monetary policy to support the fixed exchange rate. Suppose the government introduces fiscal reforms and begins to reduce its bud- get deficit D by raising taxes T. (a) [4 marks] Following the fiscal reforms, use the IS-LM-BP diagram to deduce whether the government must buy or sell domestic currency to maintain the fixed exchange rate. (b) [6 marks] Find the new point of internal and external equilibrium in the IS- LM-BP diagram. What is the effect of the reforms on GDP? Do they help in reducing the country's current-account deficit? (c) [5 marks] What difference would it make to your answers in part (b) if the government allows the exchange rate to float freely at the same time as in- troducing the fiscal reforms? Now suppose the fiscal reforms also have the effect of reducing fears of default, which implies a lower risk premium s. Continue to assume a fixed exchange rate. (d) [5 marks] Use the IS-LM-BP diagram to find whether or not this leads to a better outcome for output and a lower current account deficit compared to part (b).(a) Find the probability mass function of AAPL after six months from now, denoted by S,. (b) Finance&, formerly Bacel & Co. :), is selling call options on AAPL with strike price $150 and maturity six months for $5.55 per share. That is, one pays $5.55 now for one share of this call option, and the payoff after six months is (S1 - 150)", where x" = max(0,x). Find the probability mass function of the call option payoff after six months from now, denoted by C. (c) Suppose Aversy has a million dollars to invest in two assets (i) the AAPL call option in (b) and (ii) the six-month T-bill. What is the optimal investment portfolio for Aversy? (Because Aversy is too risk-averse, he decided to avoid investing in the stock itself.) Problem 3 (30 points) (Quadratic stock) The return of a stock seems to depend on the market return in a quadratic manner, i.e. r = a + b/ + of