Chapter 5: Production

If output is produced according to Q = K^1/2 + 3L^1/2, then this production process exhibits:

decreasing returns to scale

It is profitable to hire units of labor as long as the value of marginal product

exceeds wage.

Marginal Revenue Product

extra revenue that results from a unit increase in the input

Long-Run

firm can vary all of its inputs

Suppose the production function is given by Q = 3K + 4L. What is the marginal product of capital when 5 units of capital and 10 units of labor are employed?

3

Suppose the production function is given by Q = K^1/2 L^1/2, and that Q = 30 and K = 25. How much labor is employed by the firm?

36

Suppose the production function is given by Q = 2K + 5L. What is the marginal product of labor when 15 units of capital and 10 units of labor are employed?

5

For the production function Q = 5.2K + 3.8L, if K = 16 and L = 12, we know that MPk is:

5.2.

Production Function

indicates maximum level of output the firm can produce for any combination of inputs

As the usage of an input increases, marginal product

initially increases then begins to decline

Whenever average product is declining with increases in input usage:

marginal product is less than average product

Returns to Scale

measures the percentage change in output resulting from a given percentage change in inputs

Production

transforms inputs into outputs

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12. Refer to Table 5-1. What is the marginal revenue product of the 4th worker?

$18

The production function for a competitive firm is Q = K^.5L^.5. The firm sells its output at a price of $10, and can hire labor at a wage of $5. Capital is fixed at one unit. The profit-maximizing quantity of labor is

1

Short-Run

one or more of the firms inputs is fixed

Suppose the production function is given by Q = 4K + 6L. What is the average product of capital when 10 units of capital and 5 units of labor are employed?

7.

Firm X sells output at a price of $8 per unit and pays labor a wage of $20 per hour. The marginal product of labor is given by: MP L = 12 - .1L. To maximize profit, the firm should utilize _____ hours of labor.

95

Output is produced according to Q = 4 LK, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5, then the cost minimizing combination of K and L capable of producing 32 units of output is:

L = 4 and K = 2

Which of the following identifies the optimal usage of inputs by a profit-maximizing firm?

Marginal product of labor/price of labor = marginal product of capital/price of capital

The absolute value of the slope of the isoquant is the:

Marginal rate of technical substitution.

Linear Production Function

Q = aL + bK + C

Marginal Cost of an Input

The amount an additional unit of input adds to the firm's total cost.

Marginal Product (MPl)

additional output produced by an additional unit of labor, all other inputs held constant

Isoquant

curve that shows all possible combinations of inputs that can produce a given level of output

If the production function is Q = KL and capital is fixed at 1 unit, then the marginal product of labor when L = 25 is

none of the above

Constant Returns to Scale

occur if a given percentage change in all inputs results in an equal percentage change in output

Increasing Returns to Scale

occur if a given percentage increase in all inputs results in a greater change in output

Decreasing Returns of Scale

occur if a given percentage increase in all inputs results in a smaller percentage increase in output

Output Elasticity

percentage change in output resulting from a 1% increase in all inputs

An isoquant represents combinations of inputs that:

produce the same level of output

An isocost line

represents the combinations of K and L that cost the firm the same amount of money.

Isocost Line

shows the combination of inputs the firms can acquire at a given total cost

The slope of an isocost line shows:

the ratio of the input prices.