Question

Explain why the MRP schedule of a resource is the firm’s demand schedule for the resource in a purely competitive product market.

Answer 1

Derived demand refers to the demand that is obtained from the demand of another good. For example, when consumers demand potted plants, they also demand for seeds and fertilizers.

The demand for the inputs used in production process can also be described as derived demand because they depend on the productivity of the input in producing the final good and on the market value of the final good that is produced. For a firm with only fixed assets, the production function rises slowly as inputs are increased.

The additional output that occurs when using an additional unit of input is hired is known as Marginal Product (MP).

When a firm has both variable resources and fixed inputs (suppose the units of capital are fixed and the units of labor hired is variable) then according to the law of diminishing marginal returns, the marginal product diminishes as more additional inputs are hired.

Marginal revenue product (MRP) can be calculated by dividing the change in total revenue (TR) by the unit change in number of inputs. So, it can be described as the change in TR due to hiring one extra unit of input. Because of diminishing marginal returns, MRP falls with increase in output.

In a perfectly competitive market, market price (P) = Marginal Revenue (MR).

MRP = Marginal Product (MP) * P

So, we can say that the worth of the additional input to the firm is the amount of additional revenue that it generates.

Similarly, inputs also have marginal revenue cost (MRC). MRC is equal to the change in Total Cost (TC) divided by the unit change in number of inputs. In purely competitive factor market, the firm is a price taker.

Therefore, MRC = price of inputs.

For example, the marginal revenue cost of labor is the price of labor i.e., wages (w), since the extra cost of hiring one additional unit of labor is w.

A firm will hire inputs as long as MRP is greater than or equal to MRC. So the firm will maximize its profits when MRP = MRC = price of input.

In a perfectly competitive market, the firm can hire all the inputs that it wants at the fixed market price and produce all the quantity that he can sell at the given market price. So, the quantity demanded solely depends on the price of the input.

So, going back to the law of diminishing marginal returns, marginal revenue product diminishes as the firm hires extra units of input which is also using fixed assets. So, the demand for the inputs used in production is also downward sloping.

Let us consider the following table where a firm produces an output that sells in a competitive market at price of $100 per unit.

Its input includes two machines (fixed assets) and workers, who can be hired on as-needed basis in the labor market, at the cost of $2800 per worker.

Machines	Labor	Output	Marginal Product of Labor	Marginal Revenue Product (MRP)	Total Wage	Marginal Resource Cost (MRC)
2	0	0	-	-	0	-
2	1	60	60	6000	2800	2800
2	2	100	40	4000	5600	2800
2	3	129	29	2900	8400	2800
2	4	148	19	1900	11200	2800
2	5	160	12	1200	14000	2800
2	6	168	8	800	16800	2800

We have calculated MP of labor, MRP of labor and MRC using the formulas that we have discussed above.

For the above table we see that, 1 worker can produce 60 units of output and each of them sells for $100, then each worker is producing $6000 with the product (Refer to the column of Marginal Revenue Product).

Now, if an additional worker can produce 40 more units, then 2 workers can produce 100 units together. Hence the 2^nd worker is producing $4000 with the product. This results in a downward sloping demand for labor where demand = MRP of labor. The MRP curve is equal to the firm's input demand curve. So, in this example, if the market is willing to pay a total of $10000, then the firm will hire 2 units of labor.

It is evident that the firm is experiencing diminishing marginal returns because each additional unit of labor contributes to a lower marginal product and hence a lower MRP. This shows that the derived demand is downward sloping because of the law of diminishing marginal returns.

The firm will maximise profit by equating MRP = MRC.

So, the firm will hire 3 units of labor because MRP >= MRC = price of input = wage = $2800. When the firm hires more than 3 workers, MRP falls below MRC. SO optimum number of workers to be hired = 3