Output in an economy is given by the production function,Y=A(UKK) 0.30 (UNN)0.70,where Y is output and A measures productivity. The capital stock K is fixed at 31, and employment N is fixed at 88. The utilization rates of capital and labor equal 1 in both 2012 and 2013. Output equals 113 in 2012 and equals 119.78 in 2013. The values of the Solow residual as measured by the parameter Aare found to be 1.7560 in 2012 and 1.8614 in 2013. Thus the growth rate of the Solow residual is 6.00%.Now suppose that betweeen 2012and 2013, utilization of labor increases by 2%, while the utilization rate of capital remains unchanged. Output in 2013 is 119.78, as it was above.Calculate the new measure of A in 2013:(Enter your response rounded to four decimal places.)Calculate the growth rate of A from 2012 to 2013:%. (Enter your response as a percentage rounded to two decimal places.)When the labor utilization rate increases, the growth rate of productivitythe growth rate of the measured Solow residual.

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Answered: Output in an economy is given by the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose the population regression model, which shows the relationship between the explanatory variables (x1 and x2) and the dependent variable y, is given by log(y) = bo +b1×1+b2x2+u Suppose the model has been estimated, and the results are as follows: log(y) = 5.1 +2.6x1+0.9x2 Fill in the blanks below with the amount of rise in y and ŷ (y_hat) driven by causes provided in each sentence, respectively. From the coefficient estimate of b2, holding x1 constant, when x2 increases by 1 unit, y rises by %, which is an approximation that becomes more inaccurate as the change in log(y) increases. However, when x2 increases by one unit, y_hat rises by exactly %. When x2 decreases by one unit, y_hat falls by exactly %.
pan's high population density has resulted in a multitude of resource-usage problems. One especially serious difficulty concerns waste removal. An article reported the development of a new compression machine for processing sewage sludge. An important part of the investigation involved relating the moisture content of compressed pellets (y, in %) to the machine's filtration rate (x, in kg-DS/m/hr). The following data was read from a graph in the article. x 125.8 98.1 201.4 147.3 145.9 124.7 112.2 120.2 161.2 178.9 159.5 145.8 75.1 151.5 144.2 125.0 198.8 133.9 y 77.9 76.8 81.5 79.8 78.2 78.3 77.5 77.0 80.1 80.2 79.9 79.0 76.9 78.2 79.5 78.1 81.5 71.0 (a) Determine the slope and intercept of the estimated regression line. (Round your answers to 5 decimal places, if needed.)slope: intercept: (b) Does there appear to be a useful linear relationship? Carry out a test using the ANOVA approach and a significance level of 0.05. State the appropriate null and alternative hypotheses.…
The number of banks in a country has been dropping steadily since 1984, and the trend in recent years has been roughly linear. The annual data for the years 1999 through 2008 can be summarized as follows, where x represents the years since 1990 and y the number of banks, in thousands. n=10 Ex-235 ²-5605 Ey-77.564 Ey²=603.80424 Exy-1810.155 a. Find an equation for the least squares line. b. Use your result from part a to predict the number of banks in the year 2020. c. If this trend continues linearly, in what year will the number of banks drop below 6200? d. Find and interpret the correlation coefficient.
A group of researchers studied the effect of acid rain on wildlife and collected n = 12 samples from streams in different States. They recorded the pH (X) of the water (i.e. units above pH 7), and the BCI, a measure of biological diversity (Y). The data obtained is summarized below. DATA: Observation 1 2 3 4 5 6 7 8 9 10 11 12 pH above 7 (X) 0.65 0.50 0.93 0.86 1.02 0.94 1.16 1.24 1.30 1.45 1.85 1.89 Units of BCI (Y) 14.5 22.9 15.8 38.3 18.9 20.0 21.4 23.8 23.6 25.2 27.3 29.4 Find the correlation coefficient between pH and BCI (round to the nearest hundredth; place your answer in the box below)
Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.016 ? = y intercept of population regression line = −7 Question: Graph the population regression line by first finding the point on the line corresponding to x = 1,000 and then the point corresponding to x = 2,000, and drawing a line through these points.
Consider the following estimated model, where the dependent variable is the log of the hourly wage: log(wage) = 0.417 - 0.238female + 0.17educ + 0.0232 exper - 0.00058exper? +0.0295tenure – 0.00059tenure? female 1 if the person is female, and 0 if the person is male educ = level of education, in years exper = level of expertise, in years tenure = duration of tenure, in years Given that the above regression model has 313 observations, then its degrees of freedom is equal to For the same levels of education, expertise, and tenure, women earn exactly % less compared to men, holding other factors fixed.
The following data gives the approximate population of the world for selected years from 1850 until2000. Year 1850 1900 1950 1980 2000 Population 1.3 (billions) 1.6 3 4.4 Assume that the population growth can be modeled with an exponential function p = bemx where x is the year and p is the population in billions. Use linearleast-squares regression to determine the constants b and m for which the function best fits the data. Use the equation to estimate the population in the year 1970.
The income of farmers depends on various factors. To predict the income of the next year, a study was undertaken and data was gathered considering as many as possible factors that might influence the yearly income. Regression methods are used to create such a prediction function, that is, we want to predict the profit for the next year. The following were determined. X₁ = SIZE - farm size recorded × 1000 hectares X₂ AGE - how long the farm has been in operation in years X3 = RATIO - the ratio of land size to field size recorded as 0.5, 0.75, 0.8 and 0.9 X4 = METHOD - rotational and non rotational method of planting Ŷ INCOME the income per year recorded in × R 1 000 000.00 The partial dataset is as follows INCOME Y 1.3 2.4 3.2 1.5 2.1 a. C. Standardized Residual Sample Quantiles 15 1.0- 0.8- 0.6- 0.4- 0.2- 0.0- 20 SIZE X₁ 25 5 8 2 1.2 1.5 Predicted Theoretical Quantiles. 45 AGE X₂ 1.1. The analyst did some exploratory analysis and below are some of the residual plots he constructed.…
Assume there is a positive linear correlation between the variable R (Return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R= 2.3t + 4.8 A. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? B. If the investment continues to grow at a constant rate, what is the expeted return rate when the investment is 7 years old? C. If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?

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