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Number of Workers
Total Physical Product (units)
Marginal Physical Product
Marginal Revenue Product
0 0
1 100
2 220
3 340
4 440
5 520
6
7
8
100
120
120
100
80
60
40
30
200
240
240
200
160
120
80
60
580
620
650
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.
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 Workers
Total Physical Product (units)
Total RevenueTPP * £2
Wage (£100) *
number of workers
Total ProfitRevenue -
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 Workers
Total Physical Product (units)
Total RevenueTPP * £2
Wage (£220) *
number of workers
Total ProfitRevenue -
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 Workers
Total Physical Product (units)
Total RevenueTPP * £2
Wage (£200) *
number of workers
Total ProfitRevenue -
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 2The 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)
£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
How many workers would be employed by the monopsonist at each of the following minimum wage rates:
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)
After minus before
NJ 20.44 21.03
PA 23.33 21.17
NJ minus PA
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)
After minus before
NJ 20.44 21.03
PA 23.33 21.17
NJ minus PA 20.44 – 23.33 =
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.
