# Consider the production function F(l,K)=3l^{.25}K^{.75} a) Find the cost-minimizing bundle and...

## Question:

Consider the production function

{eq}F(l,K)=3l^{.25}K^{.75} {/eq}

a) Find the cost-minimizing bundle and the long-run total cost if w = 64 and v = 1 and total output = q = 36.

b) Change the price of capital to 3, and the price of labor to 192. Find the cost-minimizing bundle and the long-run total cost.

## Constrained Cost Minimization:

Costs can be minimized constrained to the level of output. This occurs when the isocost line is tangent to the isoquant curve. This is where optimal combination of inputs minimizes the costs.

## Answer and Explanation: 1

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View this answer**(a).**

We set up a cost minimization as the following:

{eq}min\,\,C=64l+k\\s.t\,\,\,3l^{0.25}k^{0.75} {/eq}

Set up a Lagrangian equation:

{eq}Z=64l...

See full answer below.

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Chapter 1 / Lesson 7Learn the definition of a production function in economics, understand the definition of a Cobb-Douglas production function and its formula, and explore some examples of Cobb-Douglas production function.

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