For each of the following choices of output, select the cost to produce it.

Question

A firm's production function follows:

Q = 2L + K

Where we are in the short run, where capital is fixed at 4 

While cost of capital is r=3 and cost of labor is w=3.

 

For each of the following choices of output, select the cost to produce it.

0 output =

1 output =

4 output =

6 output =

8 output =

(options: 18, 4, 12, 20, 6, 15, 0)

Answer 1

Given the production function Q = 2L + K, and the fact that we're in the short run where capital is fixed at 4, we can substitute K into the equation:

Q = 2L + 4

Let's solve for L (the quantity of labor) in terms of Q (the quantity of output):

2L = Q - 4

L = (Q - 4)/2

The cost of labor is w = 3, and the cost of capital is r = 3. Given that capital is fixed at 4 units, the cost of capital is 4r = 12. The total cost (TC) to produce a quantity Q is the cost of labor (wL) plus the cost of capital (r*K), which is 12 in this case.

TC = wL + rK

TC = 3*(Q - 4)/2 + 12

Let's calculate the total cost for each specified output level:

0 output:

TC = 3*(0 - 4)/2 + 12

TC = 3*(-4)/2 + 12

TC = -6 + 12

TC = 6 (option)

1 output:

Since the production function indicates that the minimum output possible with zero labor is 4 (when Q = 2*0 + 4), it's not feasible to produce an output of 1 with the given production function and fixed capital. Therefore, there's no cost applicable for this output level.

4 output:

TC = 3*(4 - 4)/2 + 12

TC = 3*0/2 + 12

TC = 0 + 12

TC = 12 (option)

6 output:

TC = 3*(6 - 4)/2 + 12

TC = 3*1 + 12

TC = 3 + 12

TC = 15 (option)

8 output:

TC = 3*(8 - 4)/2 + 12

TC = 3*2 + 12

TC = 6 + 12

TC = 18 (option)

So, the costs associated with the respective output levels are:

0 output = 6

1 output = Not applicable with the given production function

4 output = 12

6 output = 15

8 output = 18