.Provide solutions to the following questions.

Part B (10points, questions 11 to 20) Listed in the table below are National Accounts data for a small country: S (billions) Consumption 400 Imports 10 Investment (gross) 40 Government purchases 100 Exports 20 Capital Consumption Allowance (CCA) 20 Statistical Discrepancy 5 Receipt of factor income from other countries 12 Payments of factor income to other countries 10 Answer the following questions (provide the correct values for each item) using data provided in the table above: 1 1. Net Exports = 12. Net Factor Income from Abroad = 13. GDP = 14. GNP = 15. NNP = 16. Consumption expenditure as a percentage of GDP = 17. Government expenditure as a percentage of GDP = Questions 18 to 20 use data in the table below: Year 1 Year 2 Price Quantity Price Quantity Oranges $5.00 100 $5.00 150 Pears $3.00 100 $4.00 75 Given the data in the table above representing the total output of a small country. Calculate Real GDP for Years 1 & 2 and the growth rate in Real GDP between the two years. Remember, use Year 2 as the base year.Ex 17.3: Fish and Coconuts, Part II Let's decentralize the model from exercise 5.2. Now, let's think of "Chuck" as two firms and one consumer. Each firm (i.e., the "fish firm" that produces good 1 and the "coconut firm" that produces good 2) has the production function f(L) = VI Both firms take the price of their good as given. The labor supply is L = 100, supplied inelastically. For simplicity, let's fix p2 = 1, and let p1 = p; so throughout this problem, we'll be interested in the equilibrium price ratio p = p1/P2. (a) Assuming the two firms take the price of their good as given, find their equilibrium profit-maximizing combinations of outputs, Y, and Y2, as a function of p. You may do this in one of two ways: . Easy way: Use the fact that the firms will produce at the point along the PPF that sets MRT = p. Remember that you found the equation of the PPF and an expression for the MRT in exercise 5.2! . Hard/thorough way: Find the firms' individual supply functions, S1(p, w) and S2(w) (since p2 = 1). Find their labor demands, and set labor demand equal to the total labor supply. Solve for the equilibrium wage rate as a function of p - that is, w*(p). Finally, plug w* (p) back into the supply functions to get Yr (p) = Si(p, w*(p)) and Y,(p) = S2(w* (p)). (b) Find the total monetary value of the fish and coconuts produced given p1 = p and py = 1: that is, evaluate M(p) = pYi(p) + Y2(p) given the functions you derived in part (a). (c) Now suppose the consumer has preferences u($1, 22) = 45 Inc1 + 1012. Find her optimal quantity of fish, X], as a function of p. (Note: because this is a quasilinear utility function, it won't be dependent on her income!) Set this equal to the equilibrium quantity of fish you found in part (a), Y; and solve for the equilibrium price ratio, p*. Note: this is a nasty quadratic equation, use a calculator or Wolfram alpha to solve! Confirm that at that price ratio, the quantity of fish and coconuts supplied (and therefore demanded) is the same as you found in question 5.2(b).1. (3 points) In Metropolis only taxicabs and privately owned automobiles are allowed to use the highway betwem the airport and downtown. The market for taxi cab service is competitive. There is a special lane for taxicabs, so taxis are always able to travel at 55 miles per hour. The demand for trips by taxi cabs depends on the taxi fare P, the average speed of a trip by private automobile on the highway E, and the price of gasoline G. The number of trips supplied by taxi cabs will depend on the taxi fare and the price of gasoline. Suppose the demand for trips by taxi is given by the equation 9* = 1000 + 50G - 4E - 4001\". The supply of trips by taxi is given by the equation 9' = 200 - 306 + 1001'. When G = 4 and E =30, nd equilibrium taxi fare. At equilibrium, what is the cross-price elasticity between gasoline and taxi cab service. 2. (2 points) Ray buys only hamburgers and bottles of root beer out of a weekly income of $100. He currently consumes 20 bottles of root beer per week, and his marginal utility ofroct bow is 6. The price ofroet beer is $2 per bottle. Currently, he also consumes 15 hamburgers per week, and his marginal utility of a hamburger is 8. Is Ray maximizing utility at his current consumption basket? If not, should he buy more hamburgers each week, or fewer? 3. (2 points) Helen's preferences over CDs {C} and sandwiches (.5) are given by DIS, C) = SC+10(S+ C), wiiMU6=S+ 10 andMUs= C+ 10.1fthe price ofaCD is $9 andthe price of a sandwich is $3, and Helen can spend a combined total of $30 each day on these goods, nd Helen's optimal consumption basket. 4. (8 points) Lou's preferences over pizza (x) and other goods (12) are given by U(x, y} = xy, with associated marginal utilities MU: = y and 1111)} = x. :1) Calculate his optimal basket as a function of Px, Py and income. {2 points) b) When P; = 1, his income is $120, calculate his income and substitution effects of a decrease in the price of food P; 'crn $4 to $3. (2 points) c) When P}! = 1, his income is $120, calculate the compensating variation of a decrease in the price of food P: from $4 to $3. (2 points} d) When P} = 1, his income is $120, calculate the equivalent variation of a decrease in the price of food Px from $4 to $3. (2 points} CHAPTER 4. ABSTRACT POINT-SET TOPOLOS 156 Every compact space is automatically locally compact, sad wanected and are connected spaces. Every discrete space . is locally connected, and are connected even though & fails to be compact Snitely many points, and fails to be connected or are-connected HE than one point. Example 79. Q) is neither locally compact, locally connected, Bor by We collected at any point r. A neighborhood ! of a point - 6 10 manager 50the open rational interval, J = [objnQ. We may take a,& to be ing (whyF), so then ] = J with respect to the subspace topology on Q. IN compact, then the closed set J C N would also be compact, but if J 's comes wiff CR. where i : Q -+ R is the inclusion map. But as a subset of R. set iJ) = J Is not closed, and hence not compact. J is also disconnected, as Example 78 slows, and a separation of J imply a separation of IV as well. Finally, since AV is not connected, it cang aro-connected. Topological Invariants Theorem 4.4.5 implies that compactness is a topological invariant, and Then rem 4.4.10 does the same for connectedness. In fact, we have defined quite few properties of spaces that are invariants, which we state presently withon further proof Proposition 4.4.12. The properties of compactness, limit point com- pactress, sequential compactness, connectedness, are-connectedness, and local versions of these properties are all topological invariants. Exercises 1. Suppose A has the cofinite topology, as defined in Example 66. Prove that every nonempty subset A C X is compact, and if X is infinite, then A is also connected. 2. Let X have a separation U. V. Prove that both U and V are closed sets. 3. Prove Theorem 4.4.3. 4. Consider the space X = N x (0, 1) as defined in Example 17. (a) Show that X is not Hausdorff. (b) List a few open sets in X. Explain why we might say that X is a "discrete" set of "indiscrete" subsets. (c) Show that X is not compact