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# Macroeconomics - Coursework Example

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Macroeconomics course work Name: College: Course: Date: 1) 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…

## Extract of sample "Macroeconomics"

Download file to see previous pages (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 ...Download file to see next pages Read More
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