AP Economics:
Factor Market FRQs
December 2015
Factor Markets FRQ
1. GW Company produces and sells hats in a perfectly competitive market at a price of $2 per
hat. Assume that labor is the only variable input and the wage rate is $15 per unit of labor
per day. The table below shows GW's short-run production function for hats.
Number of workers
per day
Output of hats
Per day
TR
MRP
MPP
0
1
2
3
4
5
6
0
-
10
20
20
10
26
52
32
16
36
72
20
10
44
88
16
8
49
98
10
5
52
104
6
3
(a) After which worker do diminishing marginal returns begin? After the
second worker
(b) Calculate the marginal physical product of the fifth worker. 5
(c) Calculate the marginal revenue product of the third worker. 20
(d) How many workers will GW hire to maximize profit? 4 (MRP>MFC of 15)
(e) If GW Company has fixed costs equal to $20, what will be the company's
short-run economic profits from hiring two workers? 2 …52-(2*15)-20=2
(f) If the price of hats increases, what will happen to the number of workers
hired in the short run? Explain. It will increase. P increases, MRP
increases (shifts right) and intersects MFC curve at higher QL
2. Assume that HZRad Company produces clock radios as shown in the short-run production
function in the table below. HZRad can sell all the clock radios it produces at a market
price of $20 each and can hire all the unskilled labor it needs at a wage of $90 per day per
worker. Assume also that labor is the only variable input.
Number of
Unskilled Workers
Hired
0
1
2
3
4
5
6
Quantity of
Radios Produced
(per day)
0
20
45
60
70
75
79
MPP
MRP
MFC
20
25
15
10
5
4
400
500
300
200
100
80
90
90
90
90
90
90
7
80
1
20
90
(a) Using the specific information above, draw a correctly labeled graph of
HZRad's current supply curve for unskilled labor.
Axes labeled W or Wage and Q
Supply Curve is horizontal line at 90
(b) What is HZRad's profit-maximizing output level? Explain. 75. Highest level
where MRP>MFC (…or MRP>MRC)
(c) Suppose that HZRad is the first company to use a new technology that
increases the productivity of its unskilled workers.
(i) How will the new technology affect the quantity of unskilled labor
HZRad hires? Explain. Quantity hired increases. Increase in MPP
causes increase in MRP (shift to right), which then intersects
horizontal supply curve at higher Q.
(ii) How will the new technology affect the wage paid to HZRad's unskilled
workers? No effect.
3. Pride Textiles produces and sells towels in a perfectly competitive market. Pride Textiles
hires its workers in a perfectly competitive labor market. Assume that the market wage
rate for workers is $80 per day.
(a) State the conditions necessary for hiring the profit-maximizing amount of
labor. MRP = MFC
(b) At the profit-maximizing level of output, suppose that the marginal product
of the last worker hired is 20 towels per day. Calculate the price of a towel.
Price = $4. $80 MFC so MRP = $80. $80 MRP / 20 towel MPP = $4 price
(c) Draw a correctly labeled graph of the labor supply and demand curves for
Pride Textiles, and show the equilibrium amount of labor hired.
Correct labels: Q on x axis and and W or Wage on Y axis
Downward sloping MRP curve
Horizontal supply curve at 80
Identify and label equilibrium amount of labor
(d) Given your answer to part (b), if the price of a towel increases, explain how
Pride's profit-maximizing quantity of labor will be affected. It increases. If
P increases, MRP increases and intersects the rising supply (MFC) curve at
a higher Q…or MRP increase, and if MRP>W, hiring increases
4. The John Lamb Company, a profit-maximizing firm producing widgets, is in a perfectly
competitive widget market. Assume John Lamb employs a fixed number of employees and
rents a machine for a variable number of hours from a perfectly competitive market.
(a) Using correctly labeled side-by-side graphs of the factor market for
machines and the John Lamb Company, show each of the following.
(i) The equilibrium rental price of machines in the factor market, labeled as
PR
(ii) John Lamb’s equilibrium rental quantity of machines, labeled as QL
(i) Correct labels: X axis Quantity and Y axis Rental, PR, Q, D and S
PR and Q at intersection of D, S
(ii) Supply curve is horizontal line at P
Demand curve is MRPM
Equilibrium QL is at intersection of MRPM and SM
(b) Assume that the popularity of widgets declines, decreasing the demand or
widgets. What will happen to each of the following?
(i) Marginal product curve for machine-hours no effect
(ii) Marginal revenue product curve for machine-hours. Explain. Decreases
(shifts to left). Demand for machine-hours is derived from demand for
product. If demand decreases, price for widgets decreases, and if
price decreases, MRP decreases.
(c) John Lamb is employing the cost-minimizing combination of inputs. The
marginal product of labor is 28 widgets per worker hour and the wage rate
is $14 per hour. The marginal product of the machine is 60 widgets per
machine-hour. What is the hourly rental price of a machine?
$30. MPPL = 28 / 14 = 2 ; MPPM must also equal 2. 60/30 = 2
5.
Number
Marginal Revenue
of Workers
Product per Day
1
2
3
4
5
6
$450
$500
$450
$400
$300
$100
The table above gives the short-run marginal revenue product of labor per day for a
perfectly competitive firm. The firm is currently selling its product at the market price of $5.
(a) Calculate the marginal (physical) product of the third worker. 90;
450 = 90 * 5 (RP = MPP * P)
(b) Define the law of diminishing marginal returns and explain why it occurs.
The MPP of a variable input decreases as use of the input increases…or, as
more of a variable input is used, output increases at a decreasing rate.
This occurs because of overuse of a fixed input
(c) Diminishing marginal returns first occur with the hiring of which worker for
the firm? Third worker
(d) What is the highest daily wage that the firm is willing to pay to hire the fifth
worker? 300
(e) What will happen to the demand for labor if the market price of the
product increases? Explain. Increases. If P increases, MRP increases
(shifts to the right).
6. Assume that the market for avocados is perfectly competitive. The typical firm is earning
positive economic profit in the short-run equilibrium.
(a) Draw a correctly labeled graph for the typical firm, illustrating the short-run
equilibrium and labeling the equilibrium market price and output PE and QE,
respectively.
Correct labels: X axis is Quantity, Y axis is Price, PE and QE
PE is horizontal line also labeled MR = D
Correctly drawn and labeled MC and ATC curves, with MC crossing ATC at its
minimum
QE is where MC intersects MR
(b)
Assume there is an increase in the market wage rate for labor, a variable
input. Show on your graph in part (a) the effect of the wage increase on the
marginal cost curve in the short run. Correctly drawn MC and higher MC1
(c) Assume that avocado producers hire workers from a perfectly competitive
labor market. Draw a graph of labor supply and demand for the typical firm
and label the supply curve MFC and the demand curve MRP. Assume the
market wage rate increases from w1 to w2. Show the effect of the wage
increase on the graph, labeling the initial quantity of labor hired QL 1 and
the new quantity of labor hired QL2.
Correctly labeled X Axis Quantity of Labor and Y Axis Wage
Correctly labeled MRP is downward sloping
Initial supply curve is horizontal line at W1 labeled MFC1
New supply curve is horizontal line at W2 labeled MFC2
Initial quantity of labor is at intersection of MFC1 and MRP and is labeled QL1
New quantity of labor is at intersection of MFC2 and MRP and is labeled QL2
QL2 should be less than QL1
7.
Woodland is a small town in which everyone works for TreeMart, the local lumber
company. TreeMart is a monopsonist in the labor market and a perfect competitor in the
lumber market. In the short run, labor is the only variable input. The labor market for
TreeMart is given in the graph above.
(a) Identify the profit-maximizing quantity of labor for TreeMart. 100
(b) Identify the wage rate TreeMart pays to hire the profit-maximizing quantity
of labor. 10
(c) Identify the quantity of labor hired in each of the following situations.
(i) TreeMart operates in a competitive labor market. 200
(ii) The government imposes a minimum wage of $12.5. Explain. 250.
Minimum wage creates horizontal supply curve at 12.5, which
intersects MRP (demand curve) where Q = 250.