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A production function is given by q = 500L + 700K. The price of capital is $120 and

the price of labor is $100. If the firm wants to produce 2,800 units of output, how
many units of capital should it use?

1 Answer

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Step-by-step explanation:

To determine how many units of capital the firm should use to produce 2,800 units of output, we can use the given production function and the prices of capital and labor.

The production function is given as:

q = 500L + 700K

where:

q = Quantity of output (2,800 units in this case)

L = Units of labor

K = Units of capital

The price of capital is $120, and the price of labor is $100.

Since the firm wants to produce 2,800 units of output, we can substitute q = 2,800 into the production function and solve for K:

2,800 = 500L + 700K

Now, we need to isolate K:

700K = 2,800 - 500L

K = (2,800 - 500L) / 700

Since we don't have the specific value of L (units of labor), we cannot calculate the exact number of units of capital (K) required to produce 2,800 units of output. To find the value of K, we would need the value of L. If you have the value of L, you can substitute it into the equation to find the corresponding value of K.

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