Chapter 8: Technology and production

Short Answer Questions

1. What is a production function?

Answer: It is a schedule that shows the highest level of output the firm can produce from a given combination of inputs.

2. Under what conditions a technology can be said to exhibit constant marginal returns?

Answer: A technology exhibits constant marginal returns when there is a range of input levels over which the marginal product of a factor remains unchanged as the amount of the factor used increases.

3. What is the Marginal Rate of Technical Substitution and what information does it provide?

Answer: It is the rate at which the available technology allows the substitution of one factor for another. It is -1 times the slope of the isoquant.

4. Consider a production process that uses two inputs K and L. If the production function corresponding to this process exhibits decreasing returns to scale, what is going to happen to output if the use of both inputs doubles?

Answer: It will increase by less than two times.

5. Briefly explain what the main intuitive difference is between the concepts of marginal returns and returns to scale.

Answer: Marginal returns are input-specific, in the sense that they reflect the impact of a change in the amount of a single factor. The degree of returns to scale, on the other hand, concerns the impact of a simultaneous change in all factors in proportion on the level of output produced.

For the remaining questions support your answers with the aid of appropriate diagrams.

6. Using appropriate diagram, explain the shape of isoquants when the factors of production are perfect substitutes.

Answer: If the factors of production (for example, petrel and gasohol) are perfect substitutes, they exhibit a constant marginal rate of substitution. As a result, the resulting isoquants are straight lines.

7. Using appropriate diagram, explain the shape of isoquants when the production requires that exactly 4 units of input X and 1 unit of input Y be used to produced one unit of output.

Answer: The number of input X is measured on the horizontal axis, and the number of input Y is on the vertical axis. When two inputs must be used together in a constant proportion, that is no factor substitution is possible, the isoquants are right angles that are placed along a ray from the origin.

8. Using appropriate diagrams, explain how the slope of the Total Product curve with respect to one factor of production, can be used to derive the marginal returns to that factor.

Answer:

The slope of the total product curve is the marginal physical product of labour. When the firm’s technology exhibits increasing marginal returns to labour, the total product curve gets steeper as we increase the quantity of labour, and the marginal physical product curve is upward sloping.

9. A firm is using a technology that exhibits increasing returns to scale to its production inputs, K and L. Using an appropriate diagram, explain how the firm’s output will  change if it doubles the use of both factors.

Answer:

When the firm doubles its inputs from using 12 units of labour and 16 units of capital to using 24 units of labour and 32 units of capital, It rises output more than doubles from 100 units of output to 240 units.

10. How would your answer to question 7 change if the production function of the firm exhibited constant returns to scale?

Answer:

Starting at point g on the -isoquant, the firm double its input levels from units of labourand units of capital to 2 units of labourand 2 units of capital, the amount of  its output doubles, increases to point h on the 2-isoquant.

Essay questions

1. Would it be unreasonable to expect that the marginal returns of a production factor vary depending on the intensity of its use? Give examples to support your answer.

Brief answer: Yes, for instance, consider an increase in the amount of labour employed in a factory. At low levels of labour, the workers would have difficulty operating the machines and ensuring a smooth flow of work through the assembly process. Starting with just a few workers, added numbers can have a larger and larger incremental effect on total product. That is, the marginal returns to labour increase. At some point, however, the usefulness of more workers starts to decline. The plant eventually has more workers than can be used on the production line, because only so many people can work with a given piece of machinery. Once that point is reached, additional workers do not make much of an incremental contribution to total output.
In other words, diminishing marginal returns to labour set in.

2. Under what conditions two production inputs are said to be perfect substitutes? Discuss the implications of your answer for the firm’s production decisions.

Brief answer: The two factors of production are said to be perfect substitutes when they exhibit a constant marginal rate of substitution. The resulting isoquants are straight lines. If the two inputs can always be substituted for each other in the production process on a one-for-one basis, the firm will decide to spend their budget on the cheaper inputs only.

3. Discuss how the length of the time horizon over which a firm makes its production decisions, may affect the shape of its isoquants.

Brief answer: Assume that labour is a variable factor for National Motors and robots are fixed. Suppose that National Motors has 200 robots installed and wants to produce 160 cars per day beginning next week. To produce 160 cars per day, the firm chooses among the input combinations lying exactly on the x160-isoquant. Since in the short run the firm’s level of capital is fixed, its input decision consists of making sure it hires just enough labour to produce the desired output. Consequently, the only available input combination on the x160-isoquant is 1,000 workers per day and 200 robots per day. In the long run, however, both labour and robots are variable, so the firm can choose from among any combination of the two that can produce 160 cars per day. The set of feasible input combinations is now given by the entire x160-isoquant.

4. A construction firm uses tractors and tractor drivers as the only inputs in their production function. Only one tractor driver is required to drive one tractor. Explain the relationship between the two production factors and using an appropriate diagram; illustrate the shape of the isoquants for this firm.

Brief answer: When two inputs must be used together in a constant proportion that is only one tractor driver is required to drive one tractor, the isoquants are right angles that are placed along a 45 degree line from the origin.

5. Assume a production process that uses two inputs, K and L. Showing your calculations; derive the relationship between the Marginal Rate of Technical Substitution and the Marginal Products of each factor of production.

Brief answer: To hold its total output level constant, the firm must choose ΔL and ΔK so that (MPPL x ΔL) just offsets (MPPK x ΔK) or (MPPL x ΔL) + (MPPK x ΔK) = 0.

The equation can be rewritten as .

Now recall that −ΔK/ΔL is the marginal rate of technical substitution. Hence, it tells us that.

In words, the marginal rate of technical substitution between two inputs is equal to the ratio of the marginal physical products of the inputs.