Company produces toy robots using capital K and labor L. A consulting company ha

Question

Company produces toy robots using capital K and labor L. A consulting company has found that the optimal output is 42 and the optimal levels of factors are K=3, L=2. Market wage rate is equal to market capital rate which is – 2. Now we are using 4 units of capital and 1 unit of labor to produce 26 toy robots. We have to draft an annual statement for the shareholders.

Check all the correct sentences from each part (see below)

Part 1
We are producing at the optimal level
We are not producing at the optimal level
Part 2
We do not need to adjust our factor consumption
We can adjust our factor consumption immediately
We cannot adjust our factor consumption immediately
We can adjust our capital consumption immediately
We can adjust our labor consumption immediately
Part 3
In the long-run we will produce 42 toy robots
In the long-run we will produce 26 toy robots
In the long-run we will produce 30 toy robots
Part 4
In the the long-run our costs will be 12

In the long-run our costs will be 10

In the long-run our costs will be 8

Part 5
In the short-run we don’t have any fixed costs
In the short-run our fixed costs are equal to 8
In the short-run our fixed costs are equal to 2
Part 6
We are sure that we are producing the current number of toy robots optimally
We aren’t sure that we are producing the current number of toy robots optimally. To check it we need to solve the problem of maximizing our
revenues
We aren’t sure that we are producing current number of toyrobots optimally. To check it we need to solve the problem of minimizing our costs

Explanation / Answer

here total cost of producing 42 units of toy is wage*quantity of labour + rent*quantity of capital

TC= 2*3 + 2*2= 10

Part 1 - Total cost of producing 26 units of toy is wage*quantity of labour + rent*quantity of capital

TC= 2*4 + 2*1= 10

We are not producing at the optimal level Because by adjusting factors of input we can produce more output that is 42 units of toy at the same cost by employing quantity of capital= 3 and units of labour=2.

Part 2 - We can adjust our labor consumption immediately because labour is variable input.

Part 3-In the long-run we will produce 42 toy robots because it is the optimal level of production.

Part 5- In the short-run our fixed costs are equal to 8. because capital is fixed in the short run and in short run we are employing 4 units of capital at the rate $2. so. 2*4= 8

Part 6- We aren’t sure that we are producing current number of toyrobots optimally. To check it we need to solve the problem of minimizing our costs.

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