Exam 6: Firms and Production
When do we mean by efficient production?
Efficient production implies that no inputs are wasted.If a given number of output is efficiently produced it is not possible to produce the same amount with less inputs.
Suppose that additional units of capital affect the marginal productivity of labor.This is not unrealistic.Word processors increase the marginal productivity of secretaries.On the other hand,robotic equipment can completely replace a worker and,thereby,lower the marginal productivity of labor.Given this possibility,determine the conditions under which isoquants will not be convex (i.e.: concave).
The slope of the isoquant equals -MPL/MPK.To be concave,the slope of the isoquant becomes steeper as L increases.For this to be the case,MPL would have to increase more than MPK as labor increases and capital falls.That means the decrease in capital causes MPL to rise more than the increase in labor causes MPL to fall.The large inverse relationship implies that capital is replacing labor for this to be the case.
A small firm in Indonesia has the following estimated production function:
ln(q)= 10 + 2.6ln(L)- 0.4(ln(L))²
Derive the firm's marginal and average product of labor as functions of q and L.What is the elasticity of output with respect to labor?
Total differentiate both sides of the function with respect to L:
(1/q)(dq/dL)= (2.6 - 0.8ln(L))(1/L)
Rearrange to get:
MP = (q/L)(2.6 - 0.8ln(L))
The AP=q/L.
The elasticity is (dq/dL)(L/q)= MP/AP = 2.6 - 0.8ln(L).
For the following, please answer "True" or "False" and explain why.
-If inputs into production cannot be substituted for each other but have to be employed in fixed proportions,isoquants are straight,downward-sloping lines.
Suppose the production function for T-shirts can be represented as q = L⁰.²⁵ K⁰.⁷⁵.Show that the isoquants for this function are convex.
A firm has the following production function:
q = (L¹/³ + K¹/³)³
a.Determine the returns to scale for this function.
b.Determine the MRTS.
c.Determine the Elasticity of Substitution.
-The above figure shows the isoquants for producing steel.Increasing returns to scale are

Long-Run Production: Two Variable Inputs
-Lectures in microeconomics can be delivered either by an instructor (labor)or a movie (capital)or any combination of both.Each minute of the instructor's time delivers the same amount of information as a minute of the movie.Which graph in the above figure best represents the isoquants for lectures in microeconomics when capital per day is on the vertical axis and labor per day is on the horizontal axis?

For the following, please answer "True" or "False" and explain why.
-If marginal productivity is decreasing as more labor is hired,then average productivity must be decreasing as well.
Long-Run Production: Two Variable Inputs
-In the above figure,Graph D with Capital on the vertical axis and labor on the horizontal axis implies that

Provide a graph and an explanation to show that the production function Q = L⁰.⁵ K⁰.⁵ has diminishing marginal product of labor but has constant returns to scale.
-The above figure shows the isoquants for producing steel.When producing between 10,000 and 20,000 tons there are

The slope of the line from the origin to a given point on the curve equals
Let the production function be q = ALᵃKᵇ.Returns to scale are equal to
Suppose the production of paved roadways can be represented as q = L⁰.⁵ + K⁰.⁵.Which of the following statements is (are)TRUE?
Long-Run Production: Two Variable Inputs
-Lectures in microeconomics can be delivered either by an instructor (labor)or a movie (capital)or any combination of both.Yet the it gets harder and harder to substitute more movies for an instructor the more movies are already used.Which graph in the above figure best represents the isoquants for lectures in microeconomics when capital per day is on the vertical axis and labor per day is on the horizontal axis?

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