Assume that the rate of investment is described by the function I(t) 12 t/3 where I(t) = dK and K denotes the stock of capital at time t and that K (0) = 100 dt %3D (i) solve the above system for the capital stock K(t) (ii) plot the time path of K(t) and comment on it.
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- Which of the following statements are correct? Select all that apply. (A) A flow variable is dependent on a specific period of time. (B) A stock variable is independent of time. The amount of capital in an economy is a stock variable. (D) The amount of investment in an economy is a flow variable.Suppose that the net investment flow is described by the equation I(t) = 3t/2 and that the initial capital stock, at time t= 0, is K(0). What is the time path of capital K? If net investment is a constant flow at I(t) = 1000 (Ghana Cedis per year), what will be the total net investment (capital formation) during a year, from t= 0 to t= 1? If I(t) = 3t/2 (thousands of Ghana Cedis per year) – a nonconstant flow – what will be the capital formation during the time interval [1, 4], that is, during the second, third, and fourth years? i) Show that the Cobb-Douglas production Q=AK*L-a where Q is total output, Kis capital stock, Lis labour stock and A and a are positive stants, exhibit constant returns to scale. ii) What returns to scale does Q=5K025 L06 exhibit?The following graph has plots of the net PW of an investment as functions of %-ge changes in the values of the input variables V1, V2, V3, V4 and V5. V1 V2 V3 50% NGƯỜ V5 -30% -20% $200,000 $150,000 $100,000 $50,000 -10% -$50,000 - -$100,000 -$150,000 0% Present Worth B. Decrease of $25,000 C. Increase of 22% D. No change can affect economic feasibility E. Decrease of 22% 10% To which two variables is the present worth most sensitive to? A. V1 and V2 B. V3 and V4 C. V4 and V5 D. V1 and V5 OE. V2 and V3 % change 20% 30% 40% 50% What is the maximum allowable change in V2 before the investment becomes un-economical? OA. Increase of $25,000
- Q50 The significance of the internal rate of return (IRR) is that it tells the firm whether it should invest in a capital project by comparing the IRR to the market rate of interest. Group of answer choices True FalseThe formula M(t) = 1.14t + 13.21 gives the approximate total revenue for a corporation, in billions of dollars, t years after 2000. The formula applies to the years 2000 through 2013. (a) Explain in practical terms the meaning of M(5). The expression M(5) is the total revenue for the corporation, in billions of dollars, in 2005.The expression M(5) is the year in which the corporation will earn 5 billion dollars. The expression M(5) is the total revenue for the corporation, in billions of dollars, in 2013.The expression M(5) is the year in which the corporation will earn 5 billion dollars more than it earned in 2000.The expression M(5) is the total revenue for the corporation, in billions of dollars, in 2000. (b) Use functional notation to express the total revenue for 2010. M (c) Calculate the total revenue in 2010. billion dollarsInduced consumption is:(a)the part of consumption which is independent of the level of income.(b)the minimum level of consumption that is financed from sources other than income.(c)The maximum level of consumption that is financed from sources other than income.(d)shown by the slope of the consumption function
- Use this method, Exponential decline model, to solve ( in petroleum economics) The production of the oil well decline exponentially, the initial flow rate is 1500 STB/day, the production rate of this well become 120 STB/day in the fourth year, find the production rate after 25 months from the beginning, find yearly production and production rate for this well for the next 4 years?George Kyparisis makes bowling bals in his Miami plant. With recent increases in his costs, he has a newfound interest in efficiency. George is interested in determining the productivity of his organization. He would like to know if his organization is maintaining the manufacturing average of a 3% increase in productivity. He has the following data representing a month from last year and an equivalent month this year: Last Year Cost Per Input Unit Now Units Produced Labor (hours) Resin (pounds) Capital Invested ($) Energy (BTU) 1,000 1,000 280 255 $10 per hour $6 per pound 1% per month $0.50 per BTU 48 43 9,000 10,000 3,000 2,850 The percent change in productivity for one month last year versus one month this year on a multifactor basis with dollars as the common denominator =% (enter your response as a percentage rounded to two decimal places).Let f(t) be the balance in a savings account at the end of t years and suppose y = f(t) satisfies the differential equation y' = 0.05y - 12,500. (a)Suppose that after one year the balance is $230,000. Is the balance increasing or decreasing at that time? At what rate is it increasing or decreasing at that time? (b)Write the differential equation in the form y' = k(y - M). (c)Describe the differential equation in words. %3D %3D (a) The balance is decreasing at a rate of $ - 1000 per year. (b) y' = .05(y - 230000) (c) Choose the correct answer below. A. The rate of change of the savings account balance is proportional to the balance at the end of t years and is always increasing. B. The rate of change of the savings account balance is proportional to the difference between the balance at the end of t years and $250,000. C. The rate of change of the savings account balance is proportional to the balance at the end of t years and is always decreasing. D. The differential equation gives the…
- Consider company ABC. Today it is 1st of January 2023 and ABC has just paid a dividend of £3 million. The expected earnings of ABC for the next 30 years are forecast to grow at a rate of 15% per annum. From 1st of January 2053 and onwards the earnings of ABC are expected to grow at a rate of 5%. The required rate of return of ABC is 12% per annum. The current dividend policy of ABC is such that they pay out 50% of its earnings as dividends (assume that they pay their dividends on 1st of January every year). a) Suppose that the dividend payout ratio is expected to stay constant in the future. What is the value of ABC stock? Show and explain your calculations and any assumptions you make. b) Just after the dividend payment on 1st of January 2043, ABC is planning to reduce their dividends and only pay out 40% of its earnings. What is the value of ABC under the new dividend policy? c) Provide a recommendation to the management of ABC as to whether they should increase/cut back on…A company manufactures two types of products A and B. The total profit from the x units o product A and y units of product B in the financial year 2020 is given by P(x.y)-8x+10y-0.001(x+xy+ y)–10000, where x and y are in thousands of units. Find the values of x and y to maximize the profit. A find the maximum value of the profit function for the year 2020.(H.W): Is this function g: R-R, g(x) = x injective? %3D