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Thread: teach me do this question pls. I think this question about economies and math

  1. #1
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    Post teach me do this question pls. I think this question about economies and math

    A firm has using two inputs to produce a single output, Q . The Firmís production function is Q = x11/2 x21/2 If input price of x1 and x2 are MYR2 and MYR8 per unit, respectively, get the necessary conditions and use it to determine :

    (a) Quantity of x1 and x​2 that minimizes the cost
    (b) Minimum cost if the firm produces output of 20 units
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    Re: teach me do this question pls. I think this question about economies and math

    Quote Originally Posted by dDmondChen View Post
    A firm has using two inputs to produce a single output, Q . The Firm’s production function is Q = x11/2 x21/2 If input price of x1 and x2 are MYR2 and MYR8 per unit, respectively, get the necessary conditions and use it to determine :

    (a) Quantity of x1 and x​2 that minimizes the cost
    (b) Minimum cost if the firm produces output of 20 units
    What is the cost function? Is it $2x_1+8x_2$?
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    Re: teach me do this question pls. I think this question about economies and math

    why need to find cost function? im using MPL/w=MPK​/r
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    Re: teach me do this question pls. I think this question about economies and math

    Quote Originally Posted by dDmondChen View Post
    why need to find cost function? im using MPL/w=MPK​/r
    Those symbols may be used in your textbook, but they are not familiar to me. I will assume that the "cost" is as I described.

    (a) Then, the cost is obviously minimized when the quantity produced is 0 and $x_1=x_2=0$.

    (b) You want to minimize $2x_1+8x_2$ given the conditions that $\sqrt{x_1x_2} = 20$. Solve for $x_2$. $x_2 = \dfrac{400}{x_1}$. Plug that in to the cost function and take the derivative with respect to $x_1$. Set the derivative equal to zero to find critical points:

    $2-\dfrac{3200}{x_1^2} = 0$

    $x_1 = 40, x_2=10$

    Next, we need to show this yields the minimum cost. The instantaneous rate of change in cost at $x_1=20$ is $2-\dfrac{3200}{400} = -6<0$ and at $x_1=80$, it is $2-\dfrac{3200}{6400} = \dfrac{3}{2}>0$. This shows that a minimum occurs at $x_1=40$, and the cost is minimized at the values we found.
    Thanks from dDmondChen
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