The Theory of Macroeconomics - Coursework Example

?Macroeconomics work College: a) Find the Marginal Rate of Substitution. (4 marks) Arc: Slope of chord MRS Y X) = - ?Y / ?X Point: slope of tangent MRS = - dY/dX along indifference curve f U(X,Y) represents preferences, U(C,l) =1/c^3 +1/l^3 du/dc =1/3c^-2/3 Marginal rate of substitution is as below (b) Find the Marginal Rate of Transformation. (4 marks) Marginal rate of transformatio is as below UNs(C , h – Ns) – wUc(C , h – Ns) = 0 (1) zFNd(K , Nd) = w (2) We have UNs(C , l) – zFNd(K , h – l)Uc(C , l) = 0 Since p = zF(K , h – l) – wNd and G = T, from the budget constraint C = zF(K , h – l) – G (c) Setting MRS=MRT, solve the resulting equation algebraically for l as a function of G. (6 marks) c)First-order conditions: Uc(C , l) – l = 0 Ul(C , l) – lzFN(K , h – l) = 0 zF(K , h – l) – G – C = 0 When the first two conditions arcombined Hence, in equilibrium MRTl,C = MRSl,C = w Which states that the Pareto optimum is the point where the indifference curve is tangent to the PPF? d) What happens to consumption, wages and output as G increases? (6 marks) After the increase in g = G/Y, the model can be able to predict a decrease in (c, w), increase in (Y,N, r), spending of Private consumption is “crowded out” by government spending increase. Output increases but welfare loss as both c, l fall.T (Besada and, Miras (2002) Question 2) a) Solve for labor supply as a function of t. (6 marks) Since w = z, we obtain the system Ul(C , l) – z(1 – t)Uc(C , l) = 0 C + G – z(h – l) = 0 Totally differentiating these gives [Ucl – z(1 – t)Ucc]dC + [Ull – z(1 – t)Ucl]dl – zUcdt = 0 dC + zdl + dG = 0 We had 2 equations from the previous sections: C = w(1 – t)(h – l) (1) C = z(h – l) – G (2) By substitution, we will have G = zt(h – l) It indicates the total spending by the government that equals total tax revenue. b) Sketch the Laffer curve for values of t from 0 to 1. (4 marks) Laffer curve c) What is the equation for t that maximizes tax revenue G? Either graphically or by other means, find this value numerically. (6 marks) The equation is as below; G = tz[h – l(t)] Basing on the curve above, the tax revenue is zero if t = 0 and t = 1 Therefore the numerical value is 0.5 Government maximizes tax revenue at t = t*. REV = REV* d) If G=0.2, find (either graphically or otherwise) the two values of l and t that satisfy this requirement. (4 marks) If G=2 then l and t is as below Question 3) Calculate the % year-to-year growth rates in each series, and graph them using a time series plot and a scatter plot (4 marks) Scatter plot Time series (b) Are they positively or negatively correlated? (3 marks) They are positively correlated c) Does one lead the other? (3 marks) Basing on the graphs it is evident that one leads to the other d) Do the same using quarterly GDP and quarterly M2. Is there any consistency between M2-IIP and M2-GDP? Explain. (10 marks) Scatter plot Time series Basing on the graphs, there is no consistency between the two. This is because there is no correlation and one doesn’t lead to the other and the range or interval between one value is to small. Question 4) (a) Draw the consumer’s budget constraint, and show the optimal choice of consumption and leisure. Is it possible that the consumer may only choose an income of X? (8 marks) Consumer budget constraint The equality above holds at point H where the curve of indifference is tangent to the budget constraint and it is not possible for the consumer to choose an income of X b) What happens when the threshold value X decreases, explaining in terms of income and substitution effects; consider the cases of (i) someone whose income was initially below X and (ii) someone whose income was initially above X. (12 marks) When the value of X threshold decrease the impact is for example marginal substitution rate diminishes over time due to there is a diminishing marginal utility principle (Becker, 1965). Question 5) (a) Show how an increase in such government spending shifts the PPF. (8 marks) In the example above, the increase in the spending of the government has 2 separate impacts on the production possibilities frontier. Firstly, the increase in government spending from G1to G2 indicates a parallel downward shift in the production possibilities frontier. Secondly, the government spending productive nature is equivalent to an increase in total productivity factor which shifts the production possibilities frontier upward as well as increasing its slope (Baumol, 1973). As indicated in the graphs above, the PPF is observed to captures the trade-off between consumption and leisure that the existing production technology avails itself to the representative consumer in the economy (Atkinson and Stern, 1979). A production possibilities frontier (PPF) usually shows the possible points of production for an economy with a certain set of technology and resources. If the technology or resources of economy change, then the ‘’production possibilities frontier’’ will have to be altered. It is observed that the production possibilities frontier has pivoted instead of creating a parallel shift. Due to the fact that the new PPF has a different slope as compared to the original one, the current opportunity cost should be different from the previous one. Production possibilities frontiers Changes are normally not symmetric or uniform. In a PPF, if the technological innovation impacts only one of the products, then the outcome is a pivoting of the curve instead of a shift. b) Show that welfare can increase, and consider income and substitution effects to assess the ambiguous effects on consumption and leisure. (12 marks) Marginally, the consumer is the one who can decides that leisure is more appropriate than consumption. This implies that the consumer now needs a bigger increase in consumption in order to work more (consume less leisure). The consumer is lazier in more intuitive language (Arrow and Enthoven, 1961). Individual will choose consumption and leisure to maximize utility. Optimal consumption is indicated by the point at which the budget line is tangent to the indifference curve. At this particular point, the Substitution Marginal Rate between leisure and consumption is equal to the rate of wage. Any other bundle of leisure and consumption with certain budget constraint would imply that the person has less utility. Rise in non labor income enables a worker to “jump” to indifference curve that is higher; hence, this shows income effect. Leisure can be taken as an inferior good or as a normal good (Cornes, 1992). When the constant of holding real income is altered by wages, there will be a change in consumption-leisure bundle, thus indicating substitution effect. The working hours can increase when the rate of wage increase if the substitution effect is more than the income effect. The working hours can decrease when the rate of wage increases if the income impact is greater than the substitution effect. Cash grants can lower the wage incentives. Work disincentives can be created by welfare programs. Welfare normally reduces labor supply by granting income to non-labor, hence in relation to this, the reservation wage will be raised (Caputo, 2001). Bibliography Arrow KJ, Enthoven AC (1961) Quasi-concave programming. Econometrica 29(4):779–800 Atkinson A, Stern N (1979) A note on the allocation of time. Econ Lett 3:119–123 Baumol W (1973) Income and substitution effects in the Linder Theorem. Q J Econ 87:629–633 Becker G (1965) A theory of the allocation of time. Econ J 75:493–517 Besada M, Miras M (2002) A note on Lagrange multipliers in the multiple constraint case. Econ Lett75(1):141–145 Besada M, Vazquez C (1999) The generalized marginal rate of substitution. J Math Econ 31:553–560 Caputo MR (2001) Further results on Lagrange multipliers with several binding constraints. Econ Lett 70:335–340 Cornes R (1992) Duality and modern economics. Cambridge University Press, New York Read More