a) Define A , K , and L
b) What does it mean that Y is proportional to A?
c) What does it mean that the marginal product of capital (MPK) and the marginal product of labor (MPL) are greater than zero? Show that the marginal products are positive in the Cobb-Douglas case.
d) What does it mean that the marginal product of capital (MPK) and the marginal product of la- bor (MPL) are decreasing? Show that the marginal products are decreasing in the Cobb-Douglas case.
e) What does it mean that the marginal product of capital (MPK) is increasing in labor? Show that the marginal product of capital increases as labor increases. Is the same true for capital?
f) Does the Cobb-Douglas production function display âconstant returns to scale?â (Doubling both inputs doubles outputs). If this is true, show it, otherwise, show it is false.
a) Define A , K , and L
b) What does it mean that Y is proportional to A?
c) What does it mean that the marginal product of capital (MPK) and the marginal product of labor (MPL) are greater than zero? Show that the marginal products are positive in the Cobb-Douglas case.
d) What does it mean that the marginal product of capital (MPK) and the marginal product of la- bor (MPL) are decreasing? Show that the marginal products are decreasing in the Cobb-Douglas case.
e) What does it mean that the marginal product of capital (MPK) is increasing in labor? Show that the marginal product of capital increases as labor increases. Is the same true for capital?
f) Does the Cobb-Douglas production function display âconstant returns to scale?â (Doubling both inputs doubles outputs). If this is true, show it, otherwise, show it is false.
Related textbook solutions
Related questions
A competitive firmâs short-run demand for labor will rise when the price of its product rises.
| True | |
| False |
As the wage rate rises, the marginal revenue product of labor increases.
| True | |
| False |
A competitive firmâs demand for labor always slopes down in the short-run, but may slope upwards or downwards in the long run.
| True | |
| False |
When labor an capital are complements in production, a higher wage will cause a firm to use more capital in the long run.
| True | |
| False |
If labor is a regressive factor, then a firmâs long-run demand for labor may or may not be downward sloping.
| True | |
| False |
The short-run demand curve for labor for a firm in any type of market for its output coincides with
| the upward-sloping portion of the marginal revenue product curve. | |
| the downward-sloping portion of the marginal revenue product curve. |
| the downward-sloping portion of the marginal product curve. | |
| the marginal labor cost curve. |
An increase in the price of labor will, in the short run, cause a competitive firmâs
| marginal cost to increase, the quantity it sells to decrease, and therefore reduce the quantity of labor demanded. | |
| price of its output to increase, leaving the quantity of labor demanded unchanged. |
| marginal revenue product of labor to decrease, and therefore reduce demand for labor. | |
| marginal revenue product of labor to increase, and therefore increase demand for labor. |
Which of the following would cause the firmâs short-run demand curve for labor to shift to the right?
| A decrease in the wage rate. | |
| An increase in the price of the firmâs product. |
| An increase in the rental rate paid to capital. | |
| A decrease in the amount of complementary capital available. |
If increased capital usage reduces the firmâs short-run demand for labor, then
| labor is a regressive factor. | |
| labor and capital are complements in production. |
| labor and capital are substitutes in production. | |
| labor is a Giffen factor. |
When is the law of demand violated for labor? That is, with regards to the law of labor demand, when does an increase in the wage not lead to a reduction in the quantity of labor demanded?
| Never. | |
| When the substitution and scale effects are in opposition, with the scale effect being the larger. |
| When labor is a regressive factor. | |
| When labor earns zero economic rent. |
If the wage rate rises, then the firmâs long-run marginal costs change, which in turn affects the firmâs output level and its employment of labor. This phenomenon is known as
| the substitution effect. | |
| the scale effect. |
| the regressive-factor effect. | |
| the factor-price effect. |
When will the scale effect of a wage increase cause a reduction in the quantity of labor demanded?
| Always. | |
| When labor is not a regressive factor. |
| When labor and capital are substitutes in production. | |
| When labor and capital are complements in production. |
Consider the usual case where a higher wage rate increases a firmsâ marginal costs. In this case, the industryâs demand curve for labor
| is more wage inelastic than the individual firmsâ demand curves would indicate. | |
| coincides with the horizontal sum of individual firmsâ demand curves. |
| contains only substitution effects but no scale effects. | |
| is horizontal at the going wage rate. |
To maximize profits, a monopolist will hire the quantity of labor at which marginal revenue product of labor
| is downward sloping and equal to the market wage rate. | |
| is downward sloping and equal to marginal labor cost. |
| minus marginal labor cost is maximized. | |
| is maximized. |
A firmâs revenue minus its factor payments equals
| zero. | |
| the profits or losses earned by the firm. |
| the quasi-rents earned by the factors of production. | |
| the firmâs total revenue. |
As the amount of labor used in production increases, total product
| increases at low levels of labor and decreases at higher levels of labor. | |
| increases at high levels of labor and decreases at low levels of labor. |
| always increases. | |
| always decreases. |
A profit-maximizing price taker will produce at a level where
| the wage equals the marginal product of labor. | |
| the marginal revenue product of labor equals the price of their output. |
| the wage rate equals the price of their output. | |
| the marginal revenue product of labor equals the wage rate. |
If the wage rate is $10 per hour and one worker can produce 2 units of output per hour, then the marginal cost of production is
| $5. | |
| $10. |
| $20. | |
| The answer cannot be determined from the information given. |
A firmâs long-run demand for labor is more wage-elastic than its short-run demand for labor.
| True | |
| False |
A monopsonistâs short-run demand curve for labor coincides with its marginal revenue product of labor curve.
| True | |
| False |
Workers will receive higher wages when an employer faces an upward-sloping supply curve for labor.
| True | |
| False |
The profit an owner receives is equivalent to the rent received for her entrepreneurial services.
| True | |
| False |
When high levels of labor are employed, total production tends to increase at a decreasing rate.
| True | |
| False |
The substitution effect on labor always decreases the quantity of labor demanded when the wage rate increases.
| True | |
| False |
A firmâs marginal revenue product of labor equals the marginal product of labor multiplied by the per-unit cost of labor.
| True | |
| False |
Tastes and preferences are relevant to individual choices for consumption but not relevant to choices for supplying labor.
| True | |
| False |
A higher wage will always cause a worker to increase the quantity of labor supplied.
| True | |
| False |
The substitution and income effects of a wage increase both cause consumption to rise.
| True | |
| False |
A workerâs labor supply may either rise or fall when nonlabor income increases, depending on whether the substitution effect or the income effect dominates.
| True | |
| False |
When an increase in marginal productivity increases workersâ nonlabor income, the effect on the quantity of labor supplied is ambiguous/uncertain.
| True | |
| False |
A technological improvement that is permanent is more likely to raise employment than one that is temporary.
| True | |
| False |
Other factors being constant, firms that provide on-the-job training to workers will tend to pay higher wages.
| True | |
| False |
If there is discrimination, employers engage in it a cost.
| True | |
| False | |
Human capital tends to increase over the course of a personâs life.
| True | |
| False |
In the indifference curve budget line model of labor supply,
| labor is measured along the horizontal axis and leisure is measured along the vertical axis. | |
| labor is measured along the horizontal axis and consumption is measured along the vertical axis. |
| consumption is measured along the horizontal axis and labor is measured along the vertical axis. | |
| consumption is measured along the horizontal axis and leisure is measured along the vertical axis. |
In the indifference curve budget line model of labor supply, the slope of the indifference curve is used to measure
| the wage rate. | |
| laborâs marginal product. |
| the workerâs nonlabor income. | |
| the marginal value of leisure. |
If a worker has chosen a quantity of labor where the marginal value of leisure exceeds the wage rate, she would be better off by
| choosing less leisure. | |
| providing fewer hours of labor. |
| providing more hours of labor. | |
| staying at this combination of labor and consumption. |
When there is an increase in the wage rate there will be
| both a substitution effect and an income effect. | |
| only a substitution effect. |
| only a substitution effect. | |
| either a substitution effect or an income effect. |
When the wage rate rises, the substitution effect leads a worker to
| increase consumption while the income effect leads to a decrease in consumption. | |
| decrease consumption while the income effect leads to an increase in consumption. |
| increase consumption, as does the income effect. | |
| substitution sleep for other leisure. |
Consider the indifference curve budget line model of labor supply, and assume consumption and leisure are both normal goods. A higher wage rate would result in
| more consumption and less leisure. | |
| a reduction in the workerâs marginal value of leisure. |
| reduced consumption if the income effect is larger than the substitution effect. | |
| increased labor only if the substitution effect outweighs the income effect. |
When the wage rate rises, a worker chooses to replace some leisure hours with work hours, even if he would remain equally well off. This phenomenon is known as
| compensating differential. | |
| the income effect. |
| the substitution effect. | |
| intertemporal substitution. |
Which of the following will shift a workerâs labor supply curve to the left?
| Higher nonlabor income. | |
| A lower wage rate, assuming the substitution effect dominates the income effect. |
| New machinery that substitutes for labor and lowers its marginal product. | |
| A decrease in the marginal value of leisure. |
Which of the following would cause a rightward shift in the labor demand curve?
| Manna from heaven. | |
| A rise in the wage rate. |
| A rise in workersâ marginal productivity. | |
| A decline in workersâ nonlabor incomes. |
When some jobs are inherently more risky or unpleasant than other jobs, different workers will be paid different wages because of
| differences in human capital. | |
| differing access to capital. |
| compensating differentials | |
| discrimination. |
Discrimination is difficult to measure empirically because
| it is hard to measure and control for differences in marginal productivity. | |
| data on racial and gender differences is rarely available. |
| discrimination is practiced by very few employers. | |
| economists find no significant wage differentials due to gender or race. |
Intertemporal substitution dictates that
| people will work less in periods of high productivity. | |
| people will spend more in periods of high productivity. |
| people will work more in periods of high productivity. | |
| people will spend less in periods of high productivity. |
A decrease in the wage rate causes the budget line to
| become flatter. | |
| become steeper. |
| shift upward. | |
| shift downward. |
An increase in the marginal productivity of labor will tend to
| shift the labor supply curve rightward if the change is temporary. | |
| result in an increase in employment if the change is temporary. |
| result in an increase in employment if the change is permanent. | |
| all of the above. |
A downward shift in a workerâs budget line is a result of
| an increase in the wage rate. | |
| a decrease in the wage rate. |
| an increase in nonlabor income. | |
| a decrease in nonlabor income |
One deficiency of the labor-leisure indifference curve analysis is that because indifference curves are always tangent to the workerâs budget line, the model cannot explain why some people choose not to work.
| True | |
| False |
