Download Week 11 - Lancaster University

ECON 100 Tutorial: Week 11
www.lancaster.ac.uk/postgrad/murphys4/
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Office: LUMS C85
Question 1(a)
The following table shows how a firm’s output of a good increases as it employs more
workers. It is assumed that all other factors of production are fixed. The firm operates
under perfect competition in both the goods and labour markets. The market price of
the good is £2.
Number of
Workers
Total Physical
Product (units)
0
0
1
100
2
220
3
340
4
440
5
6
7
8
520
580
620
650
Marginal Physical
Product
Marginal Revenue
Product
100
200
120
240
120
240
100
200
80
160
60
120
40
80
30
60
Question
1(b)
How many workers will
the firm employ (to
maximise profits), if the
wage rate were:
(i) £100 per week?
6
To find this, we want to
find where does the
Marginal Cost per
Worker equal the
Marginal Revenue
Product.
(Lecture 28-29, Slide 9)
# of
Wor
kers
Total
Physical
Product
(units)
Total
Revenue
TPP * £2
Wage
(£100) *
number of
workers
Total Profit
Revenue Wages
0
0
£0
£0
£0
1
100
£200
£100
£100
2
220
£440
£200
£240
3
340
£680
£300
£380
4
440
£880
£400
£480
5
520
£1040
£500
£540
6
580
£1160
£600
£560
7
620
£1240
£700
£540
8
650
£1300
£800
£500
Question 1(b)
How many workers will
the firm employ (to
maximise profits), if the
wage rate were:
(i) £100 per week?
6
(ii) £220 per week?
3
# of
Wor
kers
Total
Physical
Product
(units)
Total
Revenue
TPP * £2
Wage
(£220) *
number of
workers
Total Profit
Revenue Wages
0
0
£0
£0
£0
1
100
£200
£220
-£20
2
220
£440
£440
£0
3
340
£680
£660
£20
4
440
£880
£880
£0
5
520
£1040
£1100
-£60
6
580
£1160
£1320
-£160
7
620
£1240
£1540
-£300
8
650
£1300
£1760
-£340
Question 1(b)
How many workers will
the firm employ (to
maximise profits), if the
wage rate were:
(i) £100 per week?
6
(ii) £220 per week?
3
(iii) £200 per week?
3 or 4
# of
Wor
kers
Total
Physical
Product
(units)
Total
Revenue
TPP * £2
Wage
(£200) *
number of
workers
Total Profit
Revenue Wages
0
0
£0
£0
£0
1
100
£200
£200
£0
2
220
£440
£400
£40
3
340
£680
£600
£80
4
440
£880
£800
£80
5
520
£1040
£1000
£40
6
580
£1160
£1200
-£40
7
620
£1240
£1400
-£160
8
650
£1300
£1600
-£300
Question 1(c)
True or False: “The demand curve for labour under perfect
competition is given by the MRP (of labour) curve.”
This statement is true for a competitive, profit-maximizing
firm. – see Lecture 28-29 slides 9-12
Note MRP and VMP are the same concept: the extra
revenue the firm gets from hiring an additional unit
of a factor of production, labor in this case.
Question 1(d)
• Will a change in each of the following lead to a
shift in or a movement along the demand
curve for labour?
– A change in the productivity of labour (MPP).
MRP of labor = MP of labor * MR, so a change in the
MP of labor will cause a shift in the labor demand.
– A change in the wage rate (W).
Wages are the price of labor, and a change in price
causes movement along a demand curve.
– A change in the price of the good (= MR)
MRP of labor = MP of labor * MR, so a change in the
MR will cause a shift in the labor demand.
Question 2
The following diagram shows a monopsony employer of labour. The
vertical axis shows costs and revenue per hour. Assume that there is
no trade union and initially that there is no minimum hourly wage rate.
Question 2(a)
How many workers will
the monopsonist
employ if it wishes to
maximise profit?
We need to find where
marginal cost =
marginal benefit.
Marginal benefit is
marginal revenue
product
So 4 workers
Question 2(b)
What hourly wage
rate will the
monopsonist pay?
This time, we find the
average cost for 4
workers. Average cost
of labor corresponds
to labor supply, so £6
is the lowest wage
that will be accepted
by at least 4 workers.
Note: Average Cost is
our Supply Curve.
Questions 2(c) & 2(d)
Assuming instead that this is an industry under perfect competition,
and that the horizontal axis is now measured in thousands, how
many workers would be employed?
In perfect
competition, Marginal
revenue product
(demand) = average
cost (supply)
So 6
What would be the
hourly wage rate
now?
£6.80
Question 2 (e)
Returning to the monopsonist, with the horizontal axis once more
measured in individual workers, assume that the government
imposes a minimum hourly wage rate. What will be the average
and marginal costs of labour at each of the following minimum
wage rates:
£5.60?
The monopsonist carries on as before, and the average cost is £6. He
was paying above minimum wage anyway, so it didn’t affect him.
Marginal cost is still £7.60
Question 2 (e)
What will be the average and marginal costs of labour at a minimum wage of
£8?
Average cost now has to increase to £8, and marginal cost is also £8, The new
marginal cost and average cost curves are now represented by the dashed line.
Question 2(f)
How many workers would be employed by the monopsonist at each of the
following minimum wage rates:
£6?
Because the original wage rate was
£6, this doesn’t have an impact and
the answer is the same as 2(a): 4
£6.80?
Read across from £6.80 to the MRP
line
Answer is 6
£7.60?
4
£8.40?
2
Question 3
Given the analysis of bilateral monopoly, if the
passing of minimum-wage legislation forces
employers to pay higher wage rates to low-paid
employees, will this necessarily cause a reduction in
employment? Use a diagram to illustrate your
answer.
Question 4
A famous research paper by David Card and Alan Krueger
from Princeton University (in New Jersey) looked at the
impact of a rise in the minimum wage in New Jersey that
occurred in 1992 (from $4.25 per hour to $5.05 per hour) on
employment - by comparing what happened to employment
in fast food restaurants before and after the change with
what had happened to employment in Pennsylvanian fast
food restaurants. The min wage in PA remained unchanged.
The table below shows the average number of (full time
equivalent) employees per restaurant.
Before
(April 92)
After
(Nov 92)
NJ
20.44
21.03
PA
23.33
21.17
NJ minus PA
After minus
before
Question 4(i)
What was the purpose of comparing what
happened in NJ with PA?
PA acts as a “control group” (sometimes this is
called a counterfactual) – it provides a guide to
what might have happened if NJ had NOT changed
the minimum wage. This depends on PA and NJ
being similar to each other. If they are, then we can
ask is what happened in PA is a good guide to what
would have happened in NJ, had NJ not increased
the minimum wage.
Question 4(ii)
Insert appropriate figures in the light grey boxes. And in
the dark grey corner box calculate a figure for how the
NJ vs PA difference had changed after the rise in the NJ
min wage.
Before
(April 92)
After
(Nov 92)
NJ
20.44
21.03
PA
23.33
21.17
NJ minus PA
20.44 – 23.33 =
After minus
before
Question 4(ii)
Before
(April 92)
After
(Nov 92)
After minus
before
NJ
20.44
21.03
0.59
PA
23.33
21.17
-2.16
NJ minus PA
-2.89
-0.14
2.75
It looks like employment in PA was falling by 2.16 (or about 9%).
This might be a good guide to what would have happened in NJ if,
like PA, the min wage had not changed.
In fact employment in NJ rose by 0.59 despite the rise in the min
wage.
So the overall effect is the difference between what happened in NJ
and what would have happened in NJ had there been no change in
min. wage. This overall effect is a 2.75 increase.
Question 4(iii)
Why is this the figure in the corner an interesting figure to
calculate? What does it show? Calculate the elasticity of
employment with respect to the minimum wage.
The difference in these changes was 2.75 (compared to an
original level of employment of 20.44) – i.e. an about 18%
rise in employment relative to PA.
The results suggest that the elasticity of employment with
respect to the min. wage is about +1 (i.e. positive rather
than negative). (the min. wage increased by 19% and the
employment went up by 18%.)
This result seems perverse - in a competitive labour
market we might expect a rise in the min wage to result in
a fall in employment.
But it would be consistent with an monopsony
interpretation of a low skilled labour market – see Q2.
Question 5(a)
The Black Death (bubonic plague) killed around half of the population of medieval
Western Europe and so reduced labour supply. Suppose England is one single (price
taking) firm that produces one type of output, Q, according to a production function;
Q=L½K½ Suppose the Black Death killed one quarter of the workforce, so L(=100) falls
to L/4. Suppose K=100.
a) How much will output fall?
For Q, L, and K after the plague, lets write Q’, L’, and K’, so L’=L/4 and K’=K
We start with: Q = L½K½
After the plague happens, Q’= L’½K’½
= (L/4)½K½
= (1/4) ½ L½K½
= (1/2) L½K½
= (1/2) Q
Output falls to half of the original level.
Question 5(b)
How much will the marginal product of labour and the
wage rise?
MPL = slope of the production function with respect to L
holding K constant.
Initially Q = L½K½ , so the rule says that
MPL = dQ/dL
= ½ L½-1K½
= ½ L-½K½
= ½ L½K½ /L
= ½ Q/L
Question 5(b)
How much will the marginal product of labour and the wage rise?
We can think of the amount of labor after the plague as L’ = ¼ L.
And we can write the productivity after the plague as Q’ = ½ Q
After the plague, Q’ = L’½K’½ , so the rule says that
MPL’ = dQ’/dL’
= ½ L’½-1K’½
= ½ L’-½K’½
= ½ L’½K’½ /L’
= ½ Q’/L’
= ½ (½ Q) / (¼ L)
= (¼ Q) / (¼ L)
= Q/L
which is double MPL= ½ Q/L.
The competitive wage rate is equal to the MPL, So wage also doubles.
Question 5(b)
How will the average productivity of labor change?
The average productivity of L is Q/L
So after the plague, average productivity is Q’/L’
Plug in L for L’, average productivity now is
Q’/L’ = ½ Q/(¼ L)
= (½ / ¼ ) * Q/L
= (1/2*4/1) * Q/L
= 2Q/L
Which is also double.