Question

Suppose you are in the photocopying business, and are using labor (L) and capital (K), in the form of copy machines. You can hire workers for $150 a week and lease copy machines for $300 a week.

(a) Suppose your current total cost of production is $3,000. Use the information above to depict the isocost you are currently operating on, carefully labeling the relevant intercepts (put L on the x-axis and K on the y-axis).

(b) You are producing 10,000 copies a week, and your current input mix is 12 workers and 4 copy machines. With your technology, assume the Marginal Rate of Technical Substitution (MRTS) between copy machines and workers at this point is 0.25 . Label this point as A on your graph. Carefully explain why you are not minimizing costs (given your production level) in A and how you would change your input mix to achieve cost minimization. Show your reasoning using isoquants/isocosts, carefully labeling points and curves and in particular depicting the cost-minimizing point B. (Note that I am obviously not looking for numbers for this point, just a graphical representation.)

(c) Assume the total cost you incur when you produce with the optimal input mix B is $2,700. Find the intercepts of the relevant isocost. Suddenly, the wage you have to pay your workers doubles (!), while the rental rate of the machines is unchanged. Draw the new isocost for the same total cost (i.e. $2,700). If you 1 want to keep your total cost the same, what happens to the amount you produce, relative to part (b)? On the other hand, if you want to keep producing the same amount, what happens to your total cost? Show your answers graphically.

(d) Let's go back to a clean slate (and a clean graph!), before the change in (c). Suppose you are now able to produce the same amount of output (say 10,000 copies) using fewer inputs. How would you represent this positive technological change using isoquants? Label the relevant isoquants with "Old" and "New" technology. Graphically show how this implies you are now producing at a lower cost (Assume input prices don't change.)

Answer 1

Suppose you are in the photocopying business, and are using labor (L) and capital (K), in the form of copy machines. You can hire workers for $150 a week and lease copy machines for $300 a week.

(a) Suppose your current total cost of production is $3,000. Use the information above to depict the isocost you are currently operating on, carefully labeling the relevant intercepts (put L on the x-axis and K on the y-axis).

Answer: Isocost curve represents all the different combinations that can be obtained from determined factors at a given cost. That is, it shows all the combinations of the factors of production that can be acquired with a given total expenditure and at given prices. In this case our total expenditure is $3,000. In order to graph the isocost, you just need two points in the curve.

You can ask the next questions:

1) If no worker is hired, what would be the maximum amount of copy machines I could get? To obtain this you just need to divide the total expenditure by the copy machines cost

10 copy machines is the maximum amount that can be purchase with the total expediture. This gives us the first point of our graph (0,10)

2) To get the next point in the graph you can ask this: If no copy machines where purchased, how many workers could you hire with the total expenditure?

Now, you must divide the total expenditure (3000) by the worker´s salary (150)

20 workers are the maximum amount of employees that could be hire if no copy machine is purchase. Now, we have the last point of the graph, (20,0). The last step is to connect the points.

Your graph should look like this: