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assume a cobb-douglas function with an alpha parameter of 0.35, and a technology level in society that doubles production. (7 points) a. complete the chart that shows the output and marginal product of labor with a fixed level of capital at 49 units at the following levels of labor: 50 workers, 100 workers, 150 workers, and 200 workers. (please use 3 decimals for all parts of the question) labor output mpl (labor level) mpl (calculus) 0 n/a n/a 50 100 150 200

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The Cobb-Douglas production function is a model of the relationship between inputs (such as labor and capital) and output in production. It takes the form:

Q = AK^alpha * L^(1-alpha)

In this case, the alpha parameter is 0.35, so 35% of output is produced with capital and 65% is produced with labor. The technology level is given as doubling production, so A = 2.

We can plug in these values and the given values for L (labor) and K (capital) to calculate output and marginal product of labor (MPL) for each labor level.

At L = 50 workers, output is:

Q = 2 * 49^0.35 * 50^0.65 = 26.28

The marginal product of labor is the additional output produced by one more unit of labor, holding all other inputs constant. It can be calculated by taking the derivative of the production function with respect to labor:

MPL = (1-alpha) * A * K^alpha * L^(-alpha)

Plugging in the values for this problem, we get:

MPL = (1-0.35) * 2 * 49^0.35 * 50^(-0.35) = 1.01

We can repeat this process for the other labor levels to complete the chart:

labor output MPL (labor level) MPL (calculus)

50         26.28            1.01            1.01

100         52.57         1.02            1.02

150         78.85         1.03            1.03

200         105.13         1.04            1.04

Learn more about Cobb-doughlas function here:

https://brainly.com/question/25672041

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