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- During the 2007–2009 recession, the value of commonstocks in real terms fell by more than 50%. How mightthis decline in the stock market have affected aggregatedemand and thus contributed to the severity of therecession? Be specific about the mechanisms throughwhich the stock market decline affected the economy.If the government collects more in tax revenue thanit spends, and households consume more than theyget in after-tax income, thena. private saving and public saving are both positive.b. private saving and public saving are bothnegative.c. private saving is positive, but public saving isnegative.d. private saving is negative, but public saving ispositive.Consider an economy with two periods (interpreted as “when young” and “when old” periods)and two consumers, Gillian Davis and Joana Wolinsky. Gillian is a star ballet dancer with a lifetime income given by ωG= (400,0). Joana is an Econ Ph.D. student with incomeωJ= (0,400). Gillian and Joana have identical utility functions given by Ui(x1,x2) = 6 lnx1+ 3 lnx2 for i=G, J a) Plot an Edgeworth box and mark the initial endowment point. b) Write the general definition of Pareto efficient allocation (one sentence) and give the equivalent condition in terms of MRS (give formula). Check if this condition is satisfied for initial endowments. c) Derive the contract curve (write down the appropriate conditions and solve for the curve) and depict it in the Edgeworth box. d) Suppose Gillian and Joana can “trade” consumption in both periods at pricesp1,p2. Find the competitive equilibrium (6 numbers) and depict the equilibrium allocation in the Edgeworth box. e) Using the MRS condition from part b),…
- Course: Macroeconomic - IS-LM Model Prove mathematically the following: Given an increase in the proportional tax on income(t), what happens to the level of output and to the tax?" . Hint: for demostration, use the IS general function for a closed economy Y = C + I + G, where C = a + c*YD and YD = Y + TR - Y*t (where t = proportional income tax) and realize changes i.e., from "t1" to "t2"3. Suppose that we have a Solow model with one twist. The twist is that thereis a government. Each period, the government consumes a fraction of output,sG. Hence, the aggregate resource constraint is:Yt = Ct + It + Gt.Where Gt = sGYt. Define private output as Ypt = Yt − Gt. Suppose thatinvestment is a constant fraction, s, of private output (consumption is then1 − s times private output). Otherwise the model is the same as in the text.104(a) Re-derive the central equation of the Solow model under this setup.(b) Suppose that the economy initially sits in a steady state. Suppose thatthere is an increase in sG that is expected to last forever. Graphicallyanalyze how this will affect the steady state value of the capital stockper worker. Plot out a graph showing how the capital stock per workerwill be affected in a dynamic senseSuppose the economy is characterized by the following behavioral equation: Y = C + I + G + (X-M) Equilibrium condition C = 2000 -f' 0.75Yd Consumption equation I = 4000 Investment expenditure G = 4100 Government Expenditure X = 2800 Export M = 400 + 0.25Y Import equation T = 100 + 0.3Y Tax equation Yd = disposable IncomeRequired: Derive Balance of Payment (BP) curve and explain why it slopes upwards Compute equilibrium national income and Imports for the economy. Differentiate between the closed-economy model and the open economy model
- Q3: Consider the national income model: Y = C + I0 + G0 + (X0 − M)............. (1) C = a + byd, (a > 0,0 < b < 1)....... (2) Yd = Y − T..................................... (3) T = T0 + ty.................................... (4) M = M0 + my................................ (5) Where: (T) = taxes, (t) = income tax rate Identify: 1/ Endogenous variable(s). 2/Exogenous variable(s). 3/ Conditional equation. 4/Behavioral equations. 5/ Definitionalequation. 6/ Constants., give the Economic meaning of them. 7/ Coefficients. give the Economic meaning of them.Julie lives for two periods. She works in the first, saves some of her income, and retires inthe second and lives off her savings. For every coconut she saves today, she earns an interestrate of r = 2%. Julie’s generation comprises of 1,000 people and each generation grows byn% relative to the previous one.a. In the first period Julie saves 100 coconuts for retirement. How many coconuts will shehave when she retires?b. Now suppose that the government implements a pay-as-you-go social security system,forcing every person in Julie’s generation to pay 100 coconuts to a social security fund thatwill distribute the money to the currently old. In exchange, when Julie retires each youngperson will pay 100 coconuts to the social security fund, and the revenue will be dividedequally among the future retirees. How much will be the revenue of the social securitysystem, and how many coconuts will each retiree will receive?c. What will have to be the range of values for n so that the government’s…) Consider the following IS-LM model set upC = 300 + 0.8(Y − 2500)I = 3500 − 400(r)G = 3000T = 2500(M/P)s = 2600Md = 2000 −1000(r) + 0.2(Y)(a) Using the IS equation, if r is 3 howmuch is Y?(b) Using the LM equation, if Y is 19000how much is r? (c) Find equilibrium r and Y, andplot IS-LM equilibrium
- (50 points) Consider the two-period economy with investment discussed in class. Forthe sake of simplicity, assume that the utility is time separable and that the per-periodutility is equal to:u(C) = log CAssume also that the technology to produce the consumption goods has constant returns to scale. Moreover, capital is the only input to production. Hence the currentperiod technology can be represented as:Y = zK1where Y , K, and z stand for output, capital and total factor productivity in the currentperiod. The future period technology is akin to the current period technology. There isno government expenditure in the current and future period so that G = 0 and G0 = 0.Finally there is full capital depreciation, namely δ = 1.(a) (10 points) Write down the social planner’s problem. State the variables withrespect to which the social planner maximises.(b) (10 points) Derive the first order conditions to the planner problem. Rearrangethere condition to find the conditions characterising the…Consider the following NIPA data for 1Q2021 (First Quarter 20210 $ billlion) Investment: Non Residential $2,948.3 Exports $2,305.3 PCE Goods $5,183.5 Investment: Residential $1,043.7 Government Expendiures Federal $1,557.0 PCE Services $9,857.7 Imports $3,152.3 Governemnt Expenditures : State and local Goernent Expenditures $2,395.9 Change in private inventories -$90.1 2a. Compute the weights of each of PCE, GPDI, NX and GOV) in GDP 2b. Consider the following rates of change (%) for each of the above items. % change PCE 10.70% GPDI -5.00% NX -6.80% GOV 6.30%In our construction of the savings and investment model, weconsidered government spending to be immediate spending. In otherwords, there was no “investment” component to government spending.Let’s change up that assumption. Suppose government spending comesin two types: investment spending (new airports, for example) aswell as government consumption (snow plowing, for example). Callthe first GI and the second GCE.