Explain the following attachments

1. (8 Points) Consider the quadratic regression problem: Yi = Bo + BIXi+ B2X? + ci. Suppose that we have 4 observations (Y1, X1), (Y2, X2), (Y3, X3), (Y4, X4) and they take values (1, 1), (0, 2), (6, 3), (7, 4). The matrix representation of this model is Y = XB + E. Then Y = (1, 0, 6, 7)T, B = (Bo, B1, B2)], and E = (61, (2, (3, EA) T. Answer the following questions with your explanation. (a) What is X in this case? (b) Calculate 3 = (XTX)-1XTY. (c) Find all the eigenvalues of XTX. (d) Is XX positive definite?2. Consider a market containing four identical firms, each of which makes an identical product. The inverse demand for this product is P = 100 - Q. The production costs for firms 1, 2, and 3 are identical and given by C(q;) = 20qi where qi is the output of firm i, i = 1,2,3. The production cost function of firm 4 is C(q4) = 30q4. Assume that the firms each choose their outputs to maximize profits given they each act as a Cournot competitor. a) Derive the Cournot equilibrium output for each firm, the product price, and the profits of all four firms. Remark: in answering (a), you can assume that firms with identical costs (firms 1, 2, and 3) will produce the same output. Under this assumption, the system of four equations (i.e., best replies) reduces to two equations in which you need to solve for firm 4's outputQuestion 4 Call Option for Expansion Project 400 Narvik Lid calculates that a new project it is considering will generate net cash inflows of $200 million but will cost $235 million to set up. However, for another $400 million dollars of outlay the project can later be expanded. The distribution of expected cash flows associated with this expansion currently has a mean of $350 million (present value), with a standard deviation of 40%. The time-frame for taking on the expansion is sometime within the next 10 years and the 10-year risk-free rate is 6 percent. Required: (a) Estimate the NPV of the initial project. (1 mark) NOV = #1 200- 235 + 40 1 0 2414 (b) Estimate the value of the expansion project, using an appropriate version of the Black Scholes option pricing model. (12 marks) (c ) What should Narvik do? Justify your answer from what you found in (a) and (b).Suppose that there is a TEMPORARY INCREASE IN THE DEMAND FOR IMPORTS that exogenous {due to changes in tastes, not due to changes in the real exchange rate or disposable income] [a]. Using AA-DD diagram for a floating exchange rate system, show what happens to national income and the exchange rate as a resutt of this temporary increase in the demand for Imports. EXPLAIN what causes any curves to shift. {b}. On another AADD diagram, show how this same temporary increase in the demand for imports would impact on national income in the short run ifthere were a FIXED EXCHANGE RATE system instead. Explain what causes any curves to shift. [c] Under which regime {floating or fixed] is the impact on national income greater? Your answer must be consistent with your previous answers In this question. [d] Suppose the exogenous increse In demand for imports were PERMANENT INSTEAD. On a diagram showing how the real exchange rate is determined using relative supply and demand curves, indicate how the increase in the demand for imports affect that diagram and determines a new real exchange rate. Show AA-DD diagram what would happen to output and the exchage rate in the short mn and the long run under a floating exchange rate system as a result of the increase in the demand for import. Assume the country begins at a long run equlibrium