Question

The production team of a furniture manufacturing company is under pressure to increase profitability to get a loan from the bank to purchase a new pattern cutting machine. At the same time, there is a waste wood chips been thrown all the way.
i. Define the company’s problem in creative ways.
ii. Suggest TWO (2) potential alternatives for your defined problem in (i).

Answer 1

1) Let us assume that the firm faces a capital constraint K-bar and labor constraint L-bar.

The first assumption is justified on the basis of everyday experience - capital pool is always finite, whether it be machinery or the financial capital needed to buy more machinery.

The second assumption is plausible on the basis of labor market rigidity - laborers are typically hired on a longer contractual basis - e.g. salaried workers are retained or let off month-to-month instead of day-to-day. The labor employment decision cannot be altered until the start of the next cycle.

Given a static production function f(L,K) {i.e. a given level of technology} and labor/capital constraints given as L-bar and K-bar, this defines the production possibility frontier (PPF) - the range of possible output combinations.

What are the outputs? There are two - units of furniture (say q1) and units of wood chips (say q2). Thus the three constraints on technology, labor and capital limit the range of choices for the output vector (q1, q2).

2) Assume that furniture and wood chips are complementary outputs. This means that even at maximal efficiency, a definite quantity of wood chips will be produced for a certain quantity of furniture units. Once again this assumption is plausible on the basis of everyday experience.

Let's say the ratio of furniture to woodchips is a:b.

Thus the PPFs are concave (upside down and rotated) L-shaped. Further, they have a kink.

3) The profit maximizing firm will select output vector to maximize profit given the exogeneous parameters p1 (the market price for a unit of furniture) and p2 (the market price for a unit of wood chips).

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Having set up the problem thus far, we can describe the firm's "problem" in terms of the relevant decision variables and their impact on profitability. Each of the three points provided above has a unique strategy associated with them.

3) Wood-chips here are an externality. The firm may or may not monetize this externality.

If it doesn't, the profit function is P = p1q1 - C(q1). But since even at maximal efficiency q1 and q2 are produced in the ratio a:b, the profit function really looks like P1 = p1q1 - C(q1, q2). {assuming for simplicity linear market demand function} The additional cost of q2, measured for example as the cost of an equivalent weight-quantity of wood, is a drain on the company's profitability. By choosing this as their profit function, they produce at a higher PPF with more furniture being produced but also greater waste.

Instead, they could choose to maximize a new profit function P2 = p1q1 + p2q2 - C(q1, q2). This would yield a different output ratio as a function of the price ratio. If this new output ratio is not equal to a:b, the efficient "kink" point is not a solution. Instead, there are two possible solutions (one for each point of intersection between the PPF and the isoprofit line). The chosen solution will be in favor of the pricier output (furniture if p1 > p2).

Thus one decision variable the firm can alter is the output vector (q1, q2) incorporating the objective of monetizing wood chips via sale.

2) The closer the ratio a : b (a measure of the company's efficiency) is to the price-ratio determined optimal output ratio, the better the firm's profitability. Thus the firm may choose to impact efficiency by investing in better managerial practices e.g. target based incentives

3) We'd assumed a static production function and fixed labor and capital supply. This assumption can be done away with by assuming the firm to choose an output maximizing input mix (L, K) subject to the constraint wL + rK = M. The firm may choose to shift the input mix in favor of better capital while laying off laborers e.g. investing in automated machinery. It should be noted that production technology (as embodied in the production function) is intellectual "capital" and thus can be treated as capital in an extended sense.