Ramsey Rule - Assignment Example

Finance and accounting [Insert al Affiliation] Question Cost –benefits analysis is one of the most sensible approaches to the assessment of global climate change problem. From the accounting cost perspective, cost-benefit analysis is the practice of identifying and quantifying the costs of undertaking an individual measure and contrasting with the benefits that can be derived from the same (Stern, 2007). It is sensible in that it makes a comparison between consequences of the projected increase in the production of the gases such as carbon and methane and the costs of policy actions that are taken currently to reduce the emission of such gases. The technique measures the costs and the benefits basing on the willing to pay or accept the compensation. This willingness is totaled up to monetary value with impacts of the environment being transformed into consumption correspondence. The costs are then discounted at a reasonable discount rate to get their present values. In the technique, there is an acceptable risk where the benefits of a particular climate policy outweigh its cost that is if the net present value is greater than zero. The environmental costs that are incurred viz.: damages due to hike in the temperature aggregating to about $140 billion (about % of the U.S. GDP). A catastrophic damage of approximately $125 and $271 billion was caused by Hurricane Katrina and sandy with overwhelming tornados that worsened hot springs droughts and summer seasons (Harris et al., 2015). The reasonable compensation costs to the economies include the cost of developing dams to prevent the damages that are caused by the water waves due to rise in the water levels. The cost of enhancing carbon sinks by encouraging reforestation and use of carbon storing agricultural methods, imposing tradable permits and pollution taxes as market-based policies to reduce carbon emission. Additionally, there is an incurrence of costs to shift the cultivation patterns to those that adopt the weather changes and to reposition people from vulnerable areas such as small coastal regions. Question 2 The pricing the future review postulates that individuals prefer consuming now than to transfer such to unknown future. Given an estimated growth cost of more than 2% in future, the risk adverse individuals prefer the current utility. The unforeseen future has difficulty in estimation of its growth due to the dynamic environment. For instance, it was anticipated that the global cost would go down due to increasing in the growth of the economy to 3.27%. This would have caused the global warming costs to downscale, but this is not the case as the global costs increase exponentially. Pricing the future dictates that the discount rates come into being after a collective decision from the society for the disparity allocation of wealth between the current and future consumptions that require the current investment. Pricing the future bases on the utility of current investment versus the current use. There is a trade-off between the current consumption (c0) and consumption at some future a date (ct). Following the current economic perception, the assumption of the total utility for any meticulous allocation is u (c0) + e-δtu (ct). In the equation, δ is the impatience rate that discounts the utility. Additionally, utility (u) takes the function of both the current and future consumption u (c) = constant (k) =(C^1-γ)/(1-γ). γ Is the relative risk aversion rate, and a zero rate displays a risk neutrality. Higher risk aversion value reflects a high risk. This because the equation displays a straight line γ =0. In this case, the utility of consumption of a given determined level of consumption (c) is the anticipated utility value u (C). Similarly, the Ramsey rule assumes that adequate wealth in that Ct = C0e^gt. Given an optimal rate of investment, the appropriate discount rate of cash flows is given by r = δ + g γ. There is an inverse correlation between the impatience rate δ and the aggregate utility of consumption u (u) in that an increase in impatience rate causes a consequent lower utility of consumption. Conversely, a low impatience rate increases the utility consumption hence the pricing the future and stern review argue in favor of the small value of δ for an increase in the utility of consumption. Question 3 Ramsey rule links the discount rate that is efficient to impatience and relative intertemporal inequality with economic growth rate. The Ramsey rule is r = δ + γg where g is the yearly growth rate between o and t dates. The law stipulates out the efficient discount rate based on the approximation of the welfare conserving rate of return on saving. The impatience rate δ =1%. Though a collective opinion is to have an impatience of zero, relative aversion to intertemporal inequality of (R=2) has been backed. According to the Ramsey rule, it is assumed that efficient discount rate should be double the consumption per capita growth rate. For instance, if the average growth rate of the per capita consumption is estimated to be 2% for each year, the fact will be justified by the use of a genuine discount rate of 4%. Conversely, stern was criticized for the choice of a minute discount rate (r=1.4%) and since the effects of the global warming cannot be considered as marginal, an ordinary evaluation method based on the present value cannot practical be used. He too measured the impact of the climate change in monetary value on the intertemporal welfare function. His choice of impatience rate was 1.0% postulated by his personal moral standards, the logarithmic utility with a risk aversion of (γ=1) which is at a lower bound estimate for R at large. The United States adopted another ambiguous model over a period of 78 years. The model was usefully only to justify differences in the rates of discount for maturity periods in years but not for maturities in terms of decades or even centuries. Therefore, the right choices for relative rate risk aversion and growth rate are γ =2% and g=2% respectively. Question 4 Ramsey rule determines the discount rate that is an efficient rate to make an equal return rate from risk-free capital. This is the interest rate that measures funds’ opportunity cost in an economy. Considering the additive of the time preferences and given two cash flows, the current cost and the future benefit at some future date is described as r = In . In the absence of market failures, the discount rate of return is the equilibrium rate of return of a bond with maturity t. The inputs in the rule are intertemporal utility U and economic growth. The Ramsey rule in Dupire’s discussion was u (c0) + e-δtu (ct). The rule needs an assumption U, which is an additive respect to the period. In the additive, the assumption is that there are two functions u and vt in that U (co,ct) = u(co) + vt (ct). The intertemporal welfare is computed by adding the immediate utility denoted by u (co) garnered by current consumption to projected utility denoted by vt (ct) produced by future consumption. This demonstrates that the current consumption is independent of the future utility consumption at time t. Since it is assumed that agents are impatient exponential discounting is taken into consideration vt (c) = exp (-δt) u(c). The function intertemporal welfare is assumed to be the aggregate of future flow of felicities at a maturity time t being f(t) = exp(-δt). More so, the intertemproral welfare when the future date is given by e – δt u( co) +e – δt(τ+ t)u(c1) = e- δt(u(co) + e- δtu(ct)) = e- δtU(co,ct). Any project that can raise the welfare U(c0, c1) the consistency guarantees the welfare increases when evaluated at a future date (- t). An additional aversion to intertemporal consumption is taken into consideration and this translates into concavity of the utility function with a measure of degree of concavity R (c ) = - . Bringing together all the elements, the efficient discount rate r = in = δ -In. Taylor made an expansion of u’ (ct) and c0 to result into r =. The equations illustrate that the efficient discount rate compose of two essentials and it is the sum of the wealth effect and rate of impatience rate respectively. Inserting ct = co exp (gt) and insertion of u’-y in the Taylors equation, the result will be r = δ + γg Question 5 According to the Ramsey rule, the r = δ + g γ where δ s the impatience rate, g is the growth rate, and γ is the relative risk of aversion (Weinberger, 2013). Adhering to the Ramsey rule, the total discount rate is arrived at by summing up the relative risk of aversion with the product of impatience rate and the annual growth rate of the economy. Question 6 The yield to maturity (YTM) is the rate of return which a bond can be redeemed at par value given that the present value of the bond is held to maturity. YTM= time period - .In the above question, the face value of the bond is assumed to be $1873; the bond has a zero coupon rate, a present value of $66.79. The time period for the bonds is 85 years just as in the previous question 85 -1 = 0.039*100 = 3.9%. It can be seen that the yield to maturity of the bonds is slightly lower than the discount rate for calculating the future costs in the previous question (Gollier, 2011). The difference is brought about as the bonds are assumed to have a zero coupon rate and; therefore, no interest is paid on yearly rather the bond is held up to maturity hence the difference in the rates. Question 7 The economic trend in the world has portrayed a substantial per capita consumption that led to increasing in the population as the welfare remained constant. The growth rate of the respective per capita consumption ranged between 1% and 2%. This substantial growth in the economy has a direct impact on the term structure of the rate of discount over the long-term. The issue of climate change and other issues such as nuclear waste have put the time into the order of a number of centuries. It is unrealistic to use historical data to form a basis for the economic growth for the future. The world of economy undergoes several transformations that cause a change in the discount rate hence it is important to include such variations in the growth in the analysis of the rate of discount. In the analysis of the extreme events on the discount rate, a flat term structure implied by random walk is assumed which involves a flat term structure. This assumption is independent of the annual growth rate distribution. Assuming that instead of an increase in the consumption rate, there is unusual random variable. Precisely, suppose we do have a small chance of a catastrophe happening. A minute possibility of a disaster causes a substantial reduction in the consumption by individuals in the economy. When the variance in the consumption is adequate, the likelihood of a catastrophe reduces the amount of the effect of wealth and raises the magnitude of the effect of precaution hence a reduction in the discount rate. According to Pindyck (2009) per capita GDP, is sensitive and inversely proportional to the probability of the disaster to happen. Examining the graph on page 67 demonstrates that given a small discount rate such as 3.6% with a catastrophe variance of 40%, the efficient discount rate declines and consequently become a negative figure. A little likelihood of a catastrophe, the individuals in the economy are to sacrifice almost all of the current wealth to avoid the experience of zero consumption at some future date (Delgado & Mohan, 2014). This is done on the ground that the marginal utility of consumption tends to become infinity when the consumption level becomes zero hence an anticipation of a reduction in discount rate given a stochastic growth rate. References Delgado, M., & Mohan, S. (2014). Integrated economic analysis. U.S. Gollier, C. (2011). Pricing the future: The economics of discounting and sustainable development. Princeton University Press, U.S. Harris, J. M., Roach, B., & Codur, A. M. (2015). The Economics of Global Climate Change. Tufts University. Pindyck, R. S. (2009). Uncertain outcomes and climate change policy’, MIT Sloan Research Paper. U.S. Stern, N. (2007). The Economics of Climate Change: The Stern Review. Cam-bridge University Press, Cambridge. Weinberger, E. D. (2013). The missing present value in the American climate prospectus. Graduate School of Management Clark University. Read More