Determine the amount of capital stock in society if output is $2700 and there are 625 workers using a Cobb-Douglas production function with an alpha parameter of 0.5 and a level of technology that doubles output, if Y = A(K^α)(L^(1-α))
Added by John H.
Close
Step 1
Since the level of technology doubles output, we can write the equation as: 2Y = A(K^α)(L^(1-α)) Dividing both sides by Y, we get: 2 = A(K^α)(L^(1-α))/Y Since Y = 2700, we can substitute this value into the equation: 2 = A(K^α)(L^(1-α))/2700 Simplifying the Show more…
Show all steps
Your feedback will help us improve your experience
Md.Daniyal Arshad and 96 other Microeconomics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The company's production is given by the Cobb-Douglas function (P(L,K)) below, where (L) is the number of units of labor, and (K) is the number of units of capital: P(L,K) = 2402 * L^k a) Find, P(16,K) b) Find, P(16,81) Which increases production more: an additional unit of labor or capital?
Adi S.
Suppose the production function of a company is given by $$ P(x, y)=250 \sqrt{x^{2}+y^{2}} $$ where $x$ represents units of labor and $y$ represents units of capital. Find the following when 6 units of labor and 8 units of capital are used. a. The marginal productivity of labor b. The marginal productivity of capital
Multivariable Calculus
Partial Derivatives
Productivity. The Cobb-Douglas production function for a petroleum company is given by $$ f(x, y)=20 x^{0.4} y^{0.6} $$ where $x$ is the utilization of labor and $y$ is the utilization of capital. If the company uses 1,250 units of labor and 1,700 units of capital, how many units of petroleum will be produced?
Functions of Several Variables
Recommended Textbooks
Principles of Economics
Principles of Microeconomics for AP® Courses
Economics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD