here are economics questions help me answer them all.its a complete kindly help mi....

Money in the Utility Function (Final, 2005) Assume that consumer's utility in period / depends on consumption and leisure: U(Cr + V(L - aN, where L is the total time available for leisure and for trips to the banks,/, is the number of trips to the bank, and a is time spent on each trip, so L - aN, is leisure. If consumers decide to spend P, C, on consumption in period , they do this at a constant rate within the period. They need money to buy goods. They get this money by going to the bank to exchange bonds for money. They can take N, such trips. If N, = 1, they go to the bank once, at the start of the period, take M, = P,C, out, and spend it over the period. Their average money balances for the period are therefore equal to M = = = P. 1. Derive average money balances as a function of spending, P,C, and the number of trips taken, N,- 2. Replace N, by its expression in terms of average real money balances and consumption in the utility function. 3. Discuss: "Putting money in the utility function is just a short cut for capturing the idea that having larger real money balances saves on trips to the bank." 4. In light of this exercise, does it make sense to assume that utility is separable in consumption and in real money balances? 5. Would money be neutral/super-neutral in this setup? Seigniorage This question asks you to extend the discussion on "Money growth, inflation, and seigniorage" in lecture to include rational expectations. Consider the basic setup presented by Olivier in class. Money demand is given by: M = exp(-ane . We are going to use the equation in discrete time, where it takes the form (in logs): m-p = -a(EPmi - P. . 1. Show that with rational expectations, the current price level is a weighted average of expected next period prices and current money supply. 2. Replace forward to show that pr is a function of expected future money supply. 3. Assume that my - mr-1 = 00. Find the evolution of the price level. A strange model of money (Waiver, 2005) Take an economy with a continuum of individuals, indexed by i, and maximizing: Cite as: Olivier Blanchard, course materials for 14.452 Macroeconomic Theory II, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. subject to: PC; + M, = P,Y + My + Ti. Individuals take Y; as given. For the economy as a whole, output is exogenous, constant, perishable, and equal to Y. The total nominal stock is constant and equal to M. 1. Derive and interpret the first order conditions for individual i. 2. Using equilibrium conditions, derive the rate of inflation in the economy. Explain in words. 3. What is the rate of money growth? Why is the rate of inflation different from the rate of money growth? 4. Would a cash in advance give rise to different results? How would you introduce it? And what would the implications on the rate of inflation?Money as a Factor of Production (Based on Dornbusch and Frenkel, 1973) The shortcut used by Dornbusch and Frenkel to introduce money in the economy is that they assume that output available is equal to a fraction of production (G(K, 1 ), where the fraction is an increasing function of real money balances: (1-1(P) ) G(K, 1 L(. satisfies these properties: L(oo = 0, L(0 = 1, L'() 0. The households maximize: Max > BUCCHI FO S.1. PHICHi + MAHI + PARKHIM = PHI(1 -L( 7,) MIL ) G(K Hi, 1 + XHi+ Mui+ PHi(1 -6 KHi where C, M. K, and X are consumption, money balances, capital holdings, and government transfers. There is no uncertainty. 1. Show that the budget constraint can be written in real terms as: Cuit (1 + MAN Hit + KHI = (1-1( MM ) )G(KAI, 1 Xhi - Miti + (1 -6 Kris PHi PHi where 1 + Multi = Phi 2. Derive the FOCs of this problem. Characterize the solution to the problem using an intertemporal and an intratemporal condition. 3. Characterize the steady state. Is money neutral? Superneutral? 4. What are the basic differences of this approach with respect to including money in the utility function or a cash in advance constraint?1 Question 1 - Jacklin's Critique to Diamond- Dygvig Take the Diamond-Dygvig model in the recitation notes, and consider Jacklin's implementation of the social optimum via a firm that pays dividends and whose shares can be sold in a spot market at { = 1. Suppose now that consumers can also directly invest in the long technology, without having to invest in the firm (that is, firms do not have the exclusivity of access to the projects). Show then that in this setting, the social optimum (cj, c;) is not implantable. In particular, show that if the firm offers a contract with dividend D = acj, a single agent may deviate by investing all his resources in the long technology at t = 0 and obtain higher utility (if the rest of the agents are actually investing all their income in shares from this firm). Answer:2 Question 2 - Public Debt and Bursting Bub- bles There's an OLG economy of agents that live only two periods. Generation born at t has preferences U (@,of) =al(@)+(1 - a) In (c) where superscript y stands for "young" and o for "old". Each agent is endowed with one unit of consumption good at birth, and has no endowment when old. Let N, be the number of agents born at time t: we assume that N = (1+9) Ne-1 where g > 0 is the growth rate of the economy (and in particular, of the endowment). Also suppose that agents can only transfer resources from t to f + 1 in a storage technology that pays 1 unit of consumption at { + 1 by unit invested of consumption at t. Borrowing and lending among consumers does not exist, since old people cannot repay young people when these are old. (a) Characterize the equilibrium allocation of the economy. Show that the allocation is not Pareto Optimal, by finding a Pareto Optimal scheme . In particular, find the "pay as you go" social insurance scheme in this economy, and show that it Pareto Dominates the equilibrium allocation.1. (27 points) For each of the following production functions, sketch a representative isoquant (2 points). Calculate the marginal product for each input, and indicate whether each marginal product is dimin- ishing, constant, or increasing (3 points). Calculate the marginal rate of technical substitution for each function (2 points). Also indicate whether the function exhibits constant, increasing, or diminishing returns to scale (2 points)- (A) F(L, K) = LX. (b) F(L, K) = L +3K (e) F(L, K) = (min ( L, K])& 2. (21 points) Consider the production function f(L, K) = 20141. (a) (15 points) Find the associated (long run) total, average, and marginal cost curves. (b) (6 points) Sketch the total, average, and marginal cost curves. 3. Problem removed due to copyright restrictions. This content is presented in audio form in the Solution Video for Problem Set 4. Problem 3. 4. (28 points) You run a cost-minimizing firm with production function f( L, K) = [min{L, A}], where [ is labor and K is capital. Assume that you are a price-taker in the input markets: you pay w for each unit of labor you hire and r for each unit of capital (where w and r are set exogenously), and face no costs other than those from labor and capital. (a) (15 points) Assuming that you can freely choose both labor and capital (ie., the "long run prob- lem"), derive expressions for your cost-minimizing conditional input demands, L*(r, w, () and K*(r, w. Q). Confirm that the conditional input demand functions are "homogeneous of degree zero" in w and r; that is, L' (tr, tw, Q) = L'(r, w,Q) ( K*(tr, tu, Q) = K* (r, w,Q) for all t > 0 (b) (8 points) What will happen to your conditional demand for labor if there is an increase in the wage rate, assuming that r and @ remain the same? Explain in one sentence why your answer makes intuitive sense. (c) (5 points) Use your answers from (a) to write down an expression for your total cost function TC(r, w. Q). Is this function "homogeneous of degree one" in w and r; that is, does TC(tr, tu, () = t . TC(r, w. Q)?1 Social Security DIscuss the validity of the following claims about Social Security. Determine whether each claim is True or False and present a concise explanation for your answer: 1. Social security is inefficient because it provides an annuity. Welfare would be improved if it paid out a lump-sum at retirement and allowed individuals to purchase annuities on their own in the free market. 2. Programs like social security, provide a work dis-incentive that is identical to the dis-incentive from an income tax because they tax individual's earnings while working 3. Many economists have found that an individual's consumption expenditure declines at the onset of retirement. Since consumption is not perfectly smoothed, this proves that agents are not fully insured against leaving the labor force. 2 Social Security Example Consider an economy that is composed of identical individuals who live for two periods. Individuals maximize: Upatient = [In(c) + =In(cz), (1) where c; is consumption in each period i. In each period there are N young individuals and N old individuals. Each individual receives an income of $300 in period 1 (their "youth" ) and no income in period 2 (their "retirement"). Individuals do not want to leave behind any money. They can save from Period 1 to Period 2 at interest rate r, and the price of consumption in each period is one. 1. Write down the individual's lifetime budget constraint, and solve to find personal savings (s*). 2. Now suppose that the Federal government institutes a social security system. The government takes $50 from each agent in Period 1, saves it, and gives it back with interest r in Period 2. Individuals are still able to privately save at interest rate r. (a) What is the terminology for this social security system? (b) What is the new equilibrium individual savings? (c) What is the effect of this social security system on social welfare? 3. Suppose that some individuals do not care about their retirement very much, and have utility functions: Uimpatient = 10 In(c,) + To In(cz). (2) The social security system still forces them to save $50. (a) If the agents can save and borrow at r, then what will their response be? (b) Suppose that these impatient agents cannot borrow because credit markets are imperfect. In that case, show that the social security system has actually made them worse off. (c) In the real world, we often observe very low savings rates. Some pundits have used this fact to justify the existence of social security, arguing that savings rates are too low. Explain how the preferences (2) versus (1) refute this story.4. Ignore for the rest of the problem the impatient agents above. The Great Depression hits this economy, and wipes out the savings of an entire generation. Consequently, the government decides to change the system so that the money coming from the younger generation is im- mediately given as benefits to the older generation. So it takes $50 from each young agent and gives it directly to an older agent. (a) What is the terminology for this social security system? (b) How much do individuals privately save now? (c) How does national savings now compare to national savings with the original social security system? 5. Finally, suppose that after the Great Depression, there is a baby boom. So where all gener- ations were the same size, now one and only one generation is twice as large as the others. (We are still using the same social security system as in part (d).) (a) When the baby boom generation is young, what are the social security benefits of the older generation as compared to the usual benefits? (b) Once the baby boom generation is old, what social security benefits does it receive compared to the usual social security benefits? (c) What could the government do to "smooth out" the effect of the baby boom? Assume that the government has no other funds that it can use to solve the problem. 6. We looked at two social security systems here: one described in part (b) and one described in part (d). (a) Which system would handle the baby boom better? Explain. (b) Why not just switch to that system today? (Brief explanation.) 3 Unemployment Insurance Consider the Unemployment Insurance (UI) program in the United States, which typically replaces 50% of a worker's wages for up to 26 weeks after job loss. Evaluate the following claims by deter- mining whether each claim is True or False and present a concise explanation for your answer: 1. The empirical observation that those receiving UI benefits remain unemployed longer than those not receiving UI benefits, conditional on unemployment, indicates that UI causes longer unemployment spells. 2. Assuming that UI causes longer unemployment spells, this clearly indicates that generosity of the program should be reduced. 3. Individual perfect experience rating - where the government effectively loans to individuals 50% of their wages while unemployed, but individuals have to repay the loan once re-employed - would result in longer unemployment durations and increased likelihood of worker layoff. 4. Assume that UI causes individuals to become more "picky" about their job choices, passing up jobs that are less pleasant or pay less wages. While everyone would like to have nice jobs, this increased picky-ness is socially inefficient. 5. Assume it is true that the extension of unemployment insurance benefits during economic downturns hinders the economy's GDP by preventing workers from going back to work and thus prolongs the length of a recession. Then, it follows that the government should not extend unemployment benefits during an economic downturn