Explore BrainMass

Explore BrainMass

    neoclassical model with diminishing returns to capital

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Help is given with various economics practice problems. See attached

    © BrainMass Inc. brainmass.com December 24, 2021, 4:46 pm ad1c9bdddf
    https://brainmass.com/economics/neoclassical-economics/neoclassical-model-with-diminishing-returns-to-capital-6769

    Attachments

    Solution Preview

    1 - The production function is:
    <br>
    <br>F(K) = A*K
    <br>
    <br>Since this functions is linear in K (that is, it is a constant -A- multiplied by K), then the first derivative is simply:
    <br>
    <br>F'(K) = A
    <br>
    <br>Now, to find the 2nd derivative, we must derive F'(K). This one is easy, because F'(K) is a constant. The derivative of a constant is zero. Therefore,
    <br>
    <br>F''(K) = 0
    <br>
    <br>
    <br>2 - We have that y=Y/N, and k=K/N. In order to find y as a function of k, we must divide both sides of the production function by N:
    <br>
    <br>Y = F(K) = A*K
    <br>Y/N = (A*K)/N
    <br> y = A*(K/N)
    <br> y = A*k
    <br>
    <br>So that's y as a function of k
    <br>
    <br>3 - Since I can't write points above letters in text mode, I'll call k' to the k with a point above it (that is, the derivative of k with respect to time). We know from the data that:
    <br>
    <br>K' = sY - delta*K
    <br>
    <br>But, since delta=0,
    <br>
    <br>K' = sY
    <br>
    <br>What we want to find here is k' (the derivative of k with respect to time) and not K', but since k=K/N, then k'=(K/N)'. So we will calculate this expression:
    <br>
    <br>k' = (K/N)' = (K'*N - K*N')/N^2
    <br>(N^2 means N squared)
    <br>
    <br>This equality comes from the fact that this is the derivative of a division. Now, since we know the expressions ...

    Solution Summary

    Is there convergence across economies?

    $2.49

    ADVERTISEMENT