1. Explain if each of the following statements is true or not: i. If average pro

Question

1. Explain if each of the following statements is true or not: i. If average product is increasing, marginal product must be less than average product.

ii. If marginal product is negative, average product must be negative.

iii. If average product is positive, total product must be increasing.

2. Suppose that a rm has the production function given by f(x1; x2) = 4?x1.?x2).( 4 squre root) Let w1 = $64 and w2 = $1. What is the total cost of producing 20 units of output in the long-run?

3. Consider the same firm as in question 2, who is facing the same input prices w1 and w2 as above. Suppose that we are now in the short-run and the firm has to use -x2 = 4. (x2 bar) What is the short-run cost of producing 72 units of output?

4. A firm produces an output using capital and labor using the production technology described by f(xL; xK) = xLxK. Let w denote the price of labor and r denote the price of capital. Assume that w = $2 and r = $1. Derive the equations for the total, average and the marginal cost functions of this firm.

Explanation / Answer

Businesses measure productivity in two ways: marginal and average. The calculation of both types often yields different answers as a result of the fundamental differences behind each measurement. In some cases, such as when a business wants to hire just one additional worker, marginal productivity is the better assessment. On the other hand, when a company is expanding and trying to assess its labor needs, average productivity is the better measurement.

Average productivity is measured by taking the total output and dividing the quantity by the number of workers. For example, if the combined number of phone calls handled in a week is 1,300 and the company has 10 employees each working the same shift length, the average productivity per worker is 130. Businesses use average productivity figures to gain a perspective on the performance of its workforce: by pooling the labor of every individual, it focuses less on how to improve a problematic worker's output and more as an estimate of the output currently being given. If low productivity is the result of a systemic issue within the company and for reasons that affect all workers, measuring average productivity as opposed to per-worker productivity is the better plan.

Marginal productivity is how much output the company gains with one extra unit of input or in this case, by having one extra worker performing the task. In some cases, adding an extra worker does not always improve productivity. If there is not enough work to go around or there isn't enough working space for everyone, productivity may decrease. Thus, firms often want to know what happens to productivity when just one incremental worker is added to the staffing roll. Eugene Diulio, author of the book, "Schaum's Outline of Theory and Problems in of Macroeconomics," explains that marginal productivity decreases if the amount of capital is fixed, or, unable to grow with the rise in workers. Charting marginal productivity helps firms assess at which point productivity is negative: this is the point at which the company stops hiring workers.

The firm's marginal and average productivity use the same figures but the outcome is expressed differently. Hypothetically, a law firm chooses to hire a filing clerk because their paperwork is growing out of control. He files 15 documents an hour. Since he cannot solve the paperwork problem alone, the firm hires another worker: The total from both workers per hour is now 45 documents. The average productivity is formed by simply dividing 45 by the two to get 22.5. Marginal productivity is different: It is the total output from the two workers minus the first, or, 45-15 which is 30. Thus, average productivity graphs the output of each worker whereas marginal productivity graphs the output from adding a worker.

Neither forms of productivity give insight on individual worker performance and statistics or the quality of technology used to perform the job which may boost productivity more than hiring workers. For instance, creating a spreadsheet macro may save each worker an hour's worth of time in data input, thereby boosting overall productivity.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.