# (solution) Please solve the question with solution. Thank you,

Please solve the question with solution. Thank you,

ECON385 Labor Economics
Problem Set 2
Due Thrusday October 6 in class (4:30pm) 1 Short Run Labor Demand Suppose that the firm has a production function described by
q= ( L3
6 0
if L &lt; 5
2
+ KL + 26K if L 5 Further suppose that we are concerned only in the short run and that the units of
capital employed are currently fixed at 8. Also, suppose that labor units are integer.
That is, they can only be in terms of whole numbers 1, 2, 3, … and so on. Suppose
that the price of each unit produced by the firm is 2.
1. Graph the M PL and the APL . Show your work. Remember that labor units are
integer, so the M PL cannot be calculated using the first derivative.
2. At what level of labor will this firm start facing diminishing marginal returns?
(Approximations to the nearest unit are admissible)
3. When will the M PL and the APL intersect?
4. Further suppose w = 145 23 . How many workers will the firm hire?
5. If w = 235 23 . How many workers will the firm hire?
6. Graph the labor demand curve for wages above 14. (Nine evenly distributed
evaluation points will su?ce)
7. Repeat question 6 with a price of each unit produced by the firm equal to 3.
8. How many more workers can the firm a?ord after the price increase of the produced good (from 2 to 3) if w = 145 23 ?
9. Calculate the elasticity of labor demand in the short run when price of each unit
produced by the firm is 2 and w changed from 145 23 to 99 23 . Show your work. 1 2 Long Run Labor Demand I Suppose we now care about the long run decisions of a firm that has a production
function of the form
1
q = 4L /2 + K
1. Calculate the MRTS
2. Do the isoquants of this production function have the diminishing MRTS quality?
Why?
3. If wage is w and the price of capital r, write the tangency condition.
4. Suppose w = 1 and r = 0.5 and the firm decides to produce 10 units of output.
(a) What are the optimal choices of inputs for this firm?
(b) What are the total costs?
5. At the same input prices, the firm chooses now to produce 20 units of output.
(a) What are the optimal choices of inputs for this firm?
(b) Do you find something unusual what compared to the optimal choices for
q = 10 in question 4a?
(c) What are the total costs?
6. Assume that, at the beginning when w0 = 1 and r = 0.5, the firm chose to produce
q0 = 20 units of output. Then, the wage increased to w1 = 2 and in consequence
the firm chose to produce q1 = 10 units of output.
(a) Calculate the optimal choices of labor and capital after the wage change.
(b) Draw the old and new isocosts lines
(c) Calculate the scale e?ect
(d) Calculate the substitution e?ect
(e) Calculate the elasticity of substitution 3 Long Run Labor Demand II Suppose we now care about the long run decisions of a firm that has a production
function of the form
q = 2L + 3K
1. Draw the isoquant that represents 20 units of output.
2 2. If the price of each unit of labor is 1, the price of each unit of capital is 2 and
the firm decides to produce 20 units of output, find the optimal choices of labor
and capital. Show all your steps. Draw the optimization problem and locate the
optimal choice in the graph.
3. If the price of each unit of labor is 2, the price of each unit of capital is 5 and the
firm decides to produce 20 units of output, find the optimal choices of labor and
capital.
4. Now suppose instead that the price of each unit of labor is 3 and the price of each
unit of capital is 4. Firm?s output is still 20. Find the optimal choices of labor
and capital. Show all your steps. Draw the optimization problem and locate the
optimal choice in the graph.
5. If the price of each unit of labor is 4, the price of each unit of capital is 5 and the
firm decides to produce 20 units of output, find the optimal choices of labor and
capital.
6. Can you find the price ratio (that is w/r) at which the optimal bundle changes?