Fiscal Policy and Consumption with Credit Constrained Consumers - Assignment Example

Running Head: Advanced Macroeconomics Advanced Macroeconomics Student’s Name College Instructor’s Name Course Name: Question 1: a generalised q-theory of investment The installation cost function which is a). To Derive a function for investment as a function of Give a brief explanation of the idea and economic mechanisms underlying the q-theory of investment. The q-theory relates to the capital used by investors and replacement cost of capital. According to the theory If the ratio of installed capital to replacement capital is less than 1 investors will want to increase their capital that is q > 1 and reduce capital if ratio is greater than 1. Explain why the q-theory is consistent with the well-documented fact that investment tends to vary negatively with the real interest rate and positively with economic activity. The variable a is part of the equation for investment (I). This is the price of the treasury bonds or the bond price. Thus total investment is the initial investment less the earnings on the bond. On the other hand, k is the total amount of the physical currency. The equation tells us that money supply is the actual physical currency less interest rate plus the consumer expenditures. Finally the variable s is the current tax rate. b). It is not is reasonable to assume that only net investment generates adjustment costs as other factors get involved in determining adjustment costs. = Since Then the value of firm is C).What is the ratio of the market value to the replacement value of the firm’s capital stock in a stationary long-run equilibrium? Furthermore, what is the relationship between the profit rate and the required return on shares in such a long-run equilibrium? Try to provide some economic intuition for your results. The stationary long-run equilibrium assumes the ratio of the market value to the replacement value of the firm’s capital stock less or equal to1 that matches with the predictable returns in being relative to variation in returns. Specifications involve the normal deviation, which has also been relatively important statistically. The results clearly indicated that the volatility processes are much persistent in establishing the superiority of the normal deviation models over the variation models. A consequence of such estimations relates to a time series and time phase that forecasts in advance about the volatility. A major objective of the equation model is to enable reliable estimation of volatility that can be utilized for different uses such as option valuation, performance measurement and portfolio allocation. Question 2: Fiscal policy and consumption with credit-constrained consumers a). At first the consumption of a poor person at budget constraint is - …………………………………………………………………(1) The consumption of a rich person at budget constraint is , 0 < < 1……………………………..(2) The population of the poor is of the total population and the total population is 1. Then the rich population is 1- Poor`s aggregate consumption = ………………………………………(3) Rich aggregate consumption = ………………………………..(4) We there add equation 3 and 4 to have The economy `s aggregate consumption C1 = + Thus derived the economy `s aggregate consumption is C1 = + C1 = - + Let us assume t be 1 C1 = - + C1 = - + C1 = Derive an expression for the economy’s marginal propensity to consume current disposable income, . C1 = + MPC = The equation shows that the marginal propensity to consume is greater than zero and there is an interest rate factor in the utility function. This means when there is change in income, there is exact change in interest rate. The function also implies that income consumption decreases when one has reduced labour supply. Compare this expression with the value of the marginal propensity to consume in an economy with no credit-constrained consumers. Explain the difference. When consumers are credit-constrained, they are left with limited money to spend for consumption purposes. And with any decline in consumption, equilibrium level of income declines. Here, initial equilibrium occurred at E0, at the intersection between the 45º Line and the C+I+G line i.e., at the intersection between the aggregate demand and aggregate supply. Initial equilibrium output was OY. However, with rise in the propensity to save, consumption level falls. Resultantly, new C+I+G line become C1+I+G. The new C1+I+G line intersect the 45º line at point E1. Equilibrium income also declines to OY1. Therefore, the rise in the marginal propensity to save actually reduces income as well as the total savings of the economy. Error: Reference source not found Paradox of thrift using injections-withdrawals Initial equilibrium occurred at E, at OY level of output, at the intersection between savings and investment. The initial equilibrium level of output is 0Y0. Now, with the rise in propensity to save, S+T line shifts upwards to S2+T and new equilibrium is set at point E1 and at a lower level of output OY1. And, as output level declines, total savings of the economy is reduced. So, with the rise in the marginal propensity to save, actual savings declines. This is indeed paradoxical in nature and was termed as paradox of thrift by Keynes. Error: Reference source not found (Boyes and Melvin, 2006, p. 248) uppose now that the government enacts a debt-financed reduction of current taxes T1 by one unit, without cutting current or planned future public consumption. Assume further that the government and the private sector have the same planning horizons, and that the private sector understands that the tax cut today will have to be matched by a tax hike tomorrow of the same present value, due to the intertemporal government budget constraint. In other words, suppose that all consumers realised that: + = 0 Consumers will try to attain the highest level of total utility possible, given their budget constraints. This consumer can maximize total utility, subject to the budget constraint. Consumer optimum is achieved when the marginal rate of substituting is just equal to the feasible, or realistic, rate of exchange between leisure and other consumption. This realistic rate is the ratio of the two prices of goods involved. It is represented by the absolute value of the value of the budget constraint, the rate at which the consumer wishes to substitute is just equal to the rate which the consumer can substitute. Here, the government incurs no additional indebtedness. Given this equal increases in government expenditure and taxes, the change in the public consumption due to a change in government expenditure is referred as the balanced budget multiplier in macroeconomics. For deriving the balanced budget multiplier, one may consider the following national income identity,=C (-T) + I +G Taking total differential, we get, dy=C1 (dy-dT) +dg (Since, investment is exogenously given, dI=0); dy, dc, dT, dG are the changes in income, consumption, tax and government expenditure respectively The second case Or, dy (1- C1) =Gg ((1- C1) Since, dG=dT as government expenditure is matched by an equal increase in tax collections. Or, dy/dG= (1- C1)/ (1- C1) =1 So, the value of the balanced budget multiplier is unity. A multiplier of one implies that output expands precisely by the increase in government expenditure with no induced consumption spending. Here, the effect of higher taxes is exactly offset the effect of the income expansion. Consequently, disposable income, and consumption remain constant. C). Derive the effect on current private consumption C1 of a temporary tax cut financed by a temporary cut in public consumption. Compare this to the effect on C1 of a permanent tax cut financed by a permanent cut in public consumption. (In the latter case you may assume that r =.) Explain the difference between your expressions. Does it make any difference for the effects of temporary and permanent tax cuts whether or not consumers are credit-constrained? From the equation above it will be noted that the consumption level will remain positive so long as there is a constant supply of wealth. Labour income tax will affect the supply of labour by a proportionate rate. If the equation above is further simplified by deriving it, the following equation will be realized. From the equation it can be noted that low labour income tax will increase labour supply in the market. If from the equation above it is clear that when V1 is greater than 0 and tax rate changes downwards, there is a similar change but in the opposite direction for the price of consumption. Therefore the tax has a huge negative impact on the equation. Question 3 Draw a diagram to illustrate the qualitative properties of the yield curve. ng logs on both sides and by estimation In (1 + i)I, we get = x x x ........x Now, to derive the Aggregate Demand Curve; The ex post real interest rate a 1 + i 1 + r + + 1 => r i - + 1 Consumption and investment are presided over by The ex ante real interest rate 1 + i 1 + i = + p r +p - + 1 Where P is a premium over the official central bank interest rate In the curve the locus of different combinations of equilibrium income and rate if interest to keep the product market in equilibrium through the equality between savings and investment . Y=C+I(r)+G, where investment is negatively related with rate of interest so that I1 Read More