Question

Asked Nov 12, 2019

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Suppose a firm uses capital (K) and labor (L) to produce widgets according to the production function Q =

K^(1/4)L^(1/4)

=
(KL)^(1/4),

where Q is output. The goal in this problem is to find the firm's total and marginal cost functions. In order to derive the cost function, the first step is to find the location of the cost-minimizing bundle on any given isoquant. To get a numerical answer, recall that the slope of an isoquant is
-MPL/MPK

(K is on the vertical axis). Using calculus, it can be shown that this slope formula reduces to -K/L. For example, consider the input bundle with K = 8, L = 2 on the isoquant with Q = 2 (note that 2 =
161/4

). The formula indicates that the slope at this point is -4 = -8/2. In fact, the formula tells us that regardless of which isoquant an input bundle is on, the slope will be -4 as long as the ratio of K to L is 4:1. Similarly, the isoquant slope will be -1 whenever the ratio of K to L is 1:1.In answering the following questions, use integer values only (don't enter unneeded decimal points).

Step 1

Step1. There was some technical problem while uploading the question. that is why I am writing the sequence of the solution and the solution is after this step. Moreover, the E part is incomplete. So I am avoiding that part.

Step 2

Step2.

Given, the production function:

Step 3

step 3. Differentiate ...

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