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### Subject 2. Productivity

Let's use labor as the input. Initially, hiring more laborers may mean more productive use of machines, which were underutilized. Output may thus initially increase. After a while, the firm may have hired too many laborers, given the number of machines. There may be overcrowding on the work floor and mistakes may result, causing productivity to fall whilst costs will increase. As units of variable input are added to a fixed input, total product will increase, first at an increasing rate and then at a declining rate. This will cause both marginal and average product curves to rise at first and then decline. Note that the marginal product curve intersects the average product curve at its maximum. The smooth curves indicate that the input can be increased by amounts of less than a single unit.

Profit Maximization

Firms demand labor, amongst other factors, to produce goods and services. The Marginal Revenue Product (MRP) of labor is the change in the total revenue of a firm that results from the employment of one additional unit of labor. The marginal revenue product of an input is equal to its marginal product multiplied by the marginal revenue of the good or service produced: MRP = MP x MR, where

• Marginal Product (MP) is the change in total output that results from the employment of one additional unit of labor.
• Marginal Revenue (MR) is the change in a firm's total revenue that results from the production and sale of one additional unit of output.

Because of the law of diminishing returns, the marginal product of labor will fall as employment of the labor expands, and thus the marginal revenue product of labor will also fall as employment expands.

The firm has two equivalent conditions for maximizing profit. They are:

• Hire the quantity of labor at which the marginal revenue product of labor (MRP) equals the wage rate (W).
• Produce the quantity of output at which marginal revenue (MR) equals marginal cost (MC).

Why?

MRP = W => MP x MR = W => MR = W/MP, since W/MP = MC => MR = MC.

This relationship indicates why wage differences across skill categories will tend to reflect productivity differences. If skilled workers are twice as productive as unskilled workers, their wage rates will tend toward twice the wage rates of unskilled workers. Low wages do not necessarily mean low cost; it is not always cheaper to hire the lowest wage workers.

Example

A mutual fund hiring research analysts is choosing among CFA charterholders and non-CFA charterholders. A CFA charterholder makes \$200,000 per year and analyzes 400 stocks per year. A non-CFA charterholder makes \$100,000 per year and can cover 100 stocks per year. Therefore, MCCFA = 200,000/400 = 500 and MCNON-CFA = 100,000/100 = 1,000.

As a result, the mutual fund will choose to hire CFA charterholders because they are twice as productive as non-CFA charterholders. This will cause the wages (price) of CFA charterholders to rise and the wages of non-CFA charterholders to fall until the ratios of the marginal product of each resource to its price (MP/P) are equal.

#### Practice Question 1

In the production of automobiles, manufacturers increase the use of robots when the wages of workers increase. This is an example of the ______.

A. output effect
B. derived demand effect
C. input substitution effect
D. labor supply effect
E. migration effect

This is an example of the input substitution effect. Firms will replace inputs that become relatively more expensive with relatively cheaper inputs.

#### Practice Question 2

If the price of a firm's output rises, then we would expect that ______

A. wages fall and employment decreases.
B. wages rise and employment increases.
C. wages rise and employment decreases.

#### Practice Question 3

If no resources had a comparative advantage in the production of any good, the production possibility curve would be ______.

A. bowed inward
B. a horizontal line
C. a downward-sloping straight line

Since there is no comparative advantage, you need not give up ever-increasing quantities of one good to gain more of another good. The opportunity cost of gaining more of one good is constant and the production possibility curve is a straight line connecting the maximum points for each good.

#### Practice Question 4

If the demand for a good is relatively inelastic, then the elasticity of demand for the labor used to produce the good will tend to be ______.

A. zero
B. relatively elastic
C. relatively inelastic