For each of the outputs, select the cost to produce it

Question

A firm's production function follows:

Q = min {4L, 2K}

Where we are in the short run, where capital is fixed at 1 

While cost of capital is r=1 and cost of labor is w=4.

 

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

Note that there are extra options that are not the answer to any item

0 output =

1 output =

2 output =

3 output =

4 output =

(options: 0, 1, 2, 3, 4, "impossible to produce with current capital")

Answer 1

In this production function, Q = min {4L, 2K}, the quantity of output (Q) depends on the lesser of 4L and 2K. Since we're in the short run and capital (K) is fixed at 1, the maximum amount of output we can produce is determined by 2K = 2*1 = 2 units.

Given the cost of capital (r) is 1 and the cost of labor (w) is 4, we can proceed to calculate the cost for each level of output. First, let's determine the amount of labor (L) needed for each level of output:

1. 0 output = 0 (no inputs needed, hence no cost)
2. 1 output = Since the production function is Q = min {4L, 2K}, we need L = 1/4 to produce 1 unit of output (because 41/4 = 1). The cost for this is wL = 4*1/4 = 1.
3. 2 output = We need L = 1/2 to produce 2 units of output (because 41/2 = 2). The cost for this is wL = 4*1/2 = 2.
4. 3 output = "impossible to produce with current capital" (because the maximum output with K = 1 is 2 units)
5. 4 output = "impossible to produce with current capital" (same reason as above)

So, matching with the options provided:

0 output = 0

1 output = 1

2 output = 2

3 output = "impossible to produce with current capital"

4 output = "impossible to produce with current capital"

0 output = 0

1 output = 1

2 output = 2

3 output = "impossible to produce with current capital"

4 output = "impossible to produce with current capital"