Y=0.5√ √N, where Y is output. K is capital, and N is the number of workers The steady-state level of capital per worker in terms of the saving rate, s, and the depreciation rate, 6, is KIN=(Property format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the character) The steady-state level of output per worker in terms of the saving rate, s, and the depreciation rate, 6, is VIN- (Property format your expression using the tools in the palette) The equation for steady-state consumption per worker in terms of the saving rate, s, and the depreciation rate, 6, is CIN- (Property format your expression using the tools in the palette)

The productivity of a country is given by ​f(x,y)=15.21x0.438y0.562​, where x is the amount of labor and y is the amount of capital.   ​(A) Find fx(x,y) and fy(x,y). ​(B) Find fx(67,55) and fy(67,55)​, and interpret the results.

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Problem 2 In class, we argued that if people could accumulate human as well as physical capital, the production function would look like the "AK" production function. (a) If the production function is AK and the savings rate is constant at rate "s", and the rates of depreciation and population growth are 8 and n respectively, what would the growth rate of the economy be? (b) What would be the macroeconomic consequences of increasing the savings rate in this economy? Explain using the model and intuitively. (c) What would be the consequences of an increase in fertility in this economy? Are these consequences good or bad? Is this answer unambiguous? (d) How are human and physical capital different from one another in the way they evolve from period to period? (e) Does human capital have an upper limit? If it does, what is the resulting production function when this is reached and the growth rate of the economy? If it doesn't have a limit, what is the resulting growth rate of output as it…

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,…

Suppose that the production function is given by Y=AK0.4N0.6. What is the percentage change in output if both capital and labor rise by 42%? Write the answer in percent terms with up to two decimals (e.g., 10.22 for 10.22%, or 2.33 for 2.33%).

Suppose that the per hour worked form of the production function for an economy is given by y = 10k03 The depreciation rate is 11%, the saving rate is 21%, and the growth rate of labor hours is 7%. The steady-state capital-labor ratio for this economy is (Round your response to two decimal places.)