10.14 Total economic output in three years. The n - vector xt denotes the economic output of a country in n different sectors, in yeart. An economist models the economic output using a linear dynamical system model xt+1 = Axt, where A is an n \times n matrix. Assuming her model is correct, find an expression for the total economic output in yeart + 3, in terms of xt and A. (The total economic output is the sum of the economic output in the n sectors.)
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10.14 Total economic output in three years. The n - vector xt denotes the economic output of a country in n different sectors, in yeart. An economist models the economic output using a linear dynamical system model xt+1 = Axt, where A is an n \times n matrix. Assuming her model is correct, find an expression for the total economic output in yeart + 3, in terms of xt and A. (The total economic output is the sum of the economic output in the n sectors.)
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- The world's population living in extreme poverty has declined linearly between the years 2005 and 2011. In 2005, the percentage of the world's population living in extreme poverty was 20.70% and in 2011, the percentage of the world's population living in extreme poverty was 13.70%. Determine a linear equation that models the world's population in extreme poverty, in percentage, as a function of years since 2005. What is the slope of this function, and what does it tell you in practical terms? Round your answer to the nearest hundredth (0.01). Om = -7.00. The world's population in extreme poverty decreased by 7 percent per year between the years 2005 and 2011. Om = 7.00. The world's population in extreme poverty increased by 7 percent per year between the years 2005 and 2011. Om = 1.17. The world's population in extreme poverty increased by 1.17 percent per year between the years 2005 and 2011. Om = -1.17. The world's population in extreme poverty decreased by 1.17 percent per year…Next, consider an economy with these equations: C = 2060 + 0.85Yd, | = 1420, G = 1220 - 0.02Y, X = 1480, M = 1525, and T = -1198 + 0.17YQ. Table provided gives data on gross domestic product (GDP) for the United States for the years 1959–2005. a. Plot the GDP data in current and constant (i.e., 2000) dollars against time. b. Letting Y denote GDP and X time (measured chronologically starting with 1 for 1959, 2 for 1960, through 47 for 2005), see if the following model fits the GDP data: Yt = β1 + β2 Xt + ut Estimate this model for both current and constant-dollar GDP. c. How would you interpret β2? d. If there is a difference between β2 estimated for current-dollar GDP and that estimated for constant-dollar GDP, what explains the difference? e. From your results what can you say about the nature of inflation in the United States over the sample period? Please answer c, d, and e. Thank you!
- Suppose that the world's current oil reserves is R = 2060 billion barrels. If, on average, the total reserves is decreasing by 15 billion barrels of oil each year, answer the following: A.) Give a linear equation for the total remaining oil reserves, R, in terms of t, the number of years since now. (Be sure to use the correct variable and Preview before you submit.) R= B.) 8 years from now, the total oil reserves will be billions of barrels. C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately years from now. (Round your answer to two decimal places.)2. Question 2: Suppose that you estimate a model of the aggregate annual retail sales of new cars that specifies that sales of new cars are a function of real disposable income, the average retail price of a car adjusted by the consumer price index, and the number of sports utility vehicles sold (you decide to add this independent variable to take account of the fact that some potential new car buyers purchase sports utility vehicles instead). You use the data (annual from 2000 to 2014) and obtain the following estimated regression equation: CARS, = 1.32 + 4.91Y D; + 0.0012 PRICE, - 7.14 SUV (2.39) (0.00045) (71.40) 1 where CARS = new car sales (in hundreds of thousands of units) in year t, YD; = real disposable income (in hundreds of billions of dollars), PRICE = the average real price of a new car in yeart (in dollars), SUV = the number of sports utility vehicles sold in year t (in millions). You expect the variable YD to have a positive coefficient and the variables PRICE and SUV to…Colton is trying to figure out when two buses traveling at different speeds will pass one another. The buses are traveling in the same direction and begin 3 miles apart. He has defined variable tt as follows: Let tt represent the time in hours. Is this a good variable definition? YES OR NO ? IF NO than explain why?
- 1) Let the growth rate of X, be defined as the log difference a (X4) = log X – log X-1. For variables X, and Y, show that the growth rate of the quotient equals the difference of the growth rates, g g(Xt) – g (Y:).Consider the two-sector macroeconomic model of a fictitious country: dy dt C = 0.5 Y + 540 I = 425 Where C = consumption; I = investment and Y = national income. = 0.034(C+I - 0.6 Y) Determine the following: (a) If Y(0) = 14,000, find an expression for Y (t) by solving the differential equation. (b) Find the time taken for income to fall to 13,000. (c) Is the system stable or unstable? Explain your answer.Consider the economic model: Yt = C +i Ct myt-1 act-1 where is GDP, c is consumption, i is investment, m and a are multipliers. (i) Write down a difference equation for y (ii) Find the condition under which the steady state exists, and find the steady state solution
- In 1928, Charles Cobb and Paul Douglas published a study in which they modeled the growth of the US economy during the period 1899 to 1922. The function used to model production was of the form: (1) P(L, K) = 6LªK!-a where P is total production (monetary value of goods produced in the year); L, the amount of work (total number of person-hours worked in a year); and K, the amount of capital invested (monetary value of machinery, equipment and buildings). In these terms, the hypotheses made by Cobb and Douglas can be stated as follows: (i) If either labor or capital cancel each other out, so does production. (ii) The marginal productivity of labor is proportional to the amount of output per unit of work. (iii) The marginal productivity of capital is proportional to the amount of production per unit of сapital. 1. The output per unit of work is (a) Tick the alternative that, for some constant a, describes the hypothesis (ii) = aP·L. = a. P () aL L P = a. (b) If we keep K constant, K = K0,…(a) Does the data on Cambodia's GDP per capita in the table correspond approximately to a linear function, an exponential function, or neither? Year 2010 2011 2012 2013 2014 2015 GDP/capita ($/person) 782.7 824.8 870.5 920.3 969.3 1020.9 The data approximately corresponds to Choose one ▼ (b) Find a formula to approximate G, the GDP per capita in dollars/person, as a function of time, t, in years since 2010. NOTE: Round your estimated coefficients to 3 decimal places. We have G(t) 2 (c) What is the approximate annual percent increase in per capita GDP? NOTE: Give your answer to 1 decimal place. GDP is increasing at approximately % per year.If the annual rate of world oil consumption t years after 1970 is modeledby the equation R(t) = 16.1e^.07t (billions of barrels per year), how much total oil (net change) was used between 1976 and 1980?