Table 7-4
-Table 7-4 shows a production relationship.Assuming the labor input is fixed at 4, what will be the optimum capital input assuming an output price of $1 and a $90-per-day cost for one unit of capital?
A)1
B)2
C)3

Question

Table 7-4  
-Table 7-4 shows a production relationship.Assuming the labor input is fixed at 4, what will be the optimum capital input assuming an output price of $1 and a $90-per-day cost for one unit of capital?
A)1 
B)2 
C)3

Quizplus · Accepted Answer

To find the optimum capital input, we need to calculate the marginal product of capital (MPC) for each level of capital input.

MPC = ∆Q/∆K

Using the data in Table 7-4, we can calculate the MPC for each level of capital input when labor is fixed at 4.

For K=1, MPC = (48-32)/(1-0) = 16 
For K=2, MPC = (92-80)/(2-1) = 12 
For K=3, MPC = (124-116)/(3-2) = 8 
For K=4, MPC = (140-136)/(4-3) = 4

Now, we need to compare the MPC to the cost of capital. The cost of capital is given as $90 per day. So, we need to choose the capital input level that gives us the highest MPC per dollar of cost.

For K=1, MPC/Cost=16/90=0.18 
For K=2, MPC/Cost=12/180=0.067 
For K=3, MPC/Cost=8/270=0.03 
For K=4, MPC/Cost=4/360=0.011

Therefore, the best choice is capital input level 3, since it has the highest MPC per dollar of cost.