esercitazione n.7 jose franchinoistituzioni di economia 2002/2003 corso c 1 chapter: 18 – the...

Jose Franchino Istituzioni di economia 2002/2003 corso C

1

Esercitazione n.7

Chapter:

18 – The Markets for the Factors of Production

Exercise n° 6


2

Esercitazione n.7

Practice Exercise n.1Firm “A” manufactures good “X”.

The following table shows for firm “A” the quantity of labor employed (hours) and the corresponding quantities of good “X” manufactured. The firm sells good “X” in a perfectly competitive market at the price of 10€; the labor market is perfectly competitive too and the hourly wage is equal to 11€

Qty of labor (hours)

Units of good X

0 01 52 103 144 175 196 207 208 19


3

Esercitazione n.7

A) Compute the marginal product of labor, the value of the marginal product and the marginal profit

MPL: the marginal product of labor is the increase of the quantity manufactured due to an increase of a unit of labor employed ( N.B. MPL is decreasing)

MPL=Q/ L

VMPL=PxMPL VMPL: the value of the marginal product is the marginal product of a factor multiplied by the price of the product (N.B. VMPL is decreasing). It represents the marginal contribution to revenues due to the increase of one unit of labor.

=VMPL - W : the marginal profit is the change in profits due to the last unity of labor employed, and is obtained as the difference between the marginal revenue (VMPL value of the marginal product), and the marginal cost (W wage).


4

Esercitazione n.7

L Q P W MPL=Q/ L

VMPL=PxMPL

=VMPL - W

0 0 10

11

--- --- ---

1 5 10

11

5 50 39

2 10

10

11

5 50 39

3 14

10

11

4 40 29

4 17

10

11

3 30 19

5 19

10

11

2 20 9

6 20

10

11

1 10 -1

7 20

10

11

0 0 -11

8 19

10

11

-1 -10 -21


5

Esercitazione n.7

Production Function

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8

Qty of labour (hours)

Qty

of

prod

uct

Production Function: the relationship between the quantity of the factor employed and the quantity manufactured of a good

B) Show graphically the production function, the marginal product, the value of the marginal product, and the marginal profit.


6

Esercitazione n.7Marginal Product of Labor

-2

-1

0

1

2

3

4

5

6

1 2 3 4 5 6 7 8


Qty

of

prod

uct

MPL:“the increase of the quantity of product due to a unit increase of the labor”

The marginal product of labor is decreasing, i.e. it decreases with the increase of the quantity of labor


7

Esercitazione n.7Value of the marginal product of labor

(labor demand curve)

-20-10

0102030405060

1 2 3 4 5 6 7 8


Val

ue in

€

VMPL:“the marginal product of labor (in units of the good) multiplied by the price of the good”


8

Esercitazione n.7

Marginal Profit

- 3 0

- 2 0

- 1 0

0

1 0

2 0

3 0

4 0

5 0

1 2 3 4 5 6 7 8


mar

gina

l pro

fit in

€

Marginal Profit:“ change of profit due to a unit increase of labor employed”


9

Esercitazione n.7Value of the marginal product of labor

(labor demand curve)

-20-10

0102030405060

1 2 3 4 5 6 7 8


Val

ue in

€

W = 11€

Optimal choice

VMPL = W

C) How much labor will be employed?

The firm in order to select the optimal quantity of labor compares the marginal revnue due to the last unit of labor (value of the marginal product) with the marginal cost of the same unit (wage). It keeps to employ new workers as long as the marginal profit is positive.


10

Esercitazione n.7Marginal Profit

- 3 0

- 2 0

- 1 0

0

1 0

2 0

3 0

4 0

5 0

1 2 3 4 5 6 7 8


mar

gina

l pro

fit in

€

>0

<0

Optimal Qty labor

MR > MC VMPL > W >0

If the marginal profit is positive, profits are increasing, and viceversa. The firm maximizes its profits by employing 5 hours of labor.


11

Esercitazione n.7

D) If the fixed cost is equal to 100€ and there is only one variable input (labor), what is the total profit of the firm?

TC = FC + VC = FC +(qty labor x wage) = 100 + (5x11) = 155

Profit = TR – TC = 190 – 155 = 35€

TR = qty manufactured x price = 19 x 10 = 190

The optimal choice of 5 units of labor at a wage of 11€, the output will therefore be 19 units of good at a price of 10€ each.


12

Esercitazione n.7E) How does the optimal choice of the firm change if the price of the product raises up to 12€?

L Q P W MPL=Q/ L

VMPL=PxMPL

=VMPL - W

0 0 12 11

--- --- ---

1 5 12 11

5 60 49

2 10 12 11

5 60 49

3 14 12 11

4 48 37

4 17 12 11

3 36 25

5 19 12 11

2 24 13

6 20 12 11

1 12 1

7 20 12 11

0 0 -11

8 19 12 11

-1 -12 -23

The firm should now employ a further unit of work as compared to the previous situation


13

Esercitazione n.7

F) What happens if the wage increase up to 15€, while the price of the good is 12€?


14

Esercitazione n.7

L Q P W MPL=Q/ L

VMPL=PxMPL

=VMPL - W

0 0 12 15

--- --- ---

1 5 12 15

5 60 45

2 10 12 15

5 60 45

3 14 12 15

4 48 33

4 17 12 15

3 36 21

5 19 12 15

2 24 9

6 20 12 15

1 12 -3

7 20 12 15

0 0 -15

8 19 12 15

-1 -12 -27

New cost of labor is 15 €, while the price of the good is 12 €.

Since the wage has increased, the employment of the sixth unit of work is not convenient anymore: the profit maximising firm will use 5 units of work.


15

Esercitazione n.7

Problem n. 3 pag. 335

Discuss the effect of each of the following events on the labor market of the computer industry:

a) The Ministry of Education buys a Personal Computer for each graduate student.

b) An increasing quantity of students graduates in engineering and in information sciences.

c) The firms manufacturing computers build new productive plants.


16

Esercitazione n.7

a) If the Ministry of Education buys a PC for each student, the demand of PC increases, the price increases as well as the value of the marginal product of the workers that manufacture computers. Therefore, the labor demand on the market of PCs increases, and it will result in an increase in the wages and in the number of employed workers.

PC Market

S

D

pri

ce

quantity

P

Labor Market

S

D

wag

en.workers

WD1

P1

D1

W1

L L1VMPL = P x MPL VMPL = P1 x

MPL


17

Esercitazione n.7b) If a greater number of students graduates in engineering and information sciences, the number of workers that would like to work for firms manufacturing computers increases. The labor supply increases, therefore the wage decreases and the number of employed workers increases.

Wage

n° workers

S

S1

D

W

W1

L1L


18

Esercitazione n.7

c) The building of new plants in this industry causes an increase in the marginal product of labor and in the value of the marginal product of labor, for all levels of labor employed. The labor demand will increase, and both the number of workers and the wage level will increase.

Wage

n° workers

S

D1

D

W

W1

L1L


19

Esercitazione n.7

Problem n. 6 pag. 396

Sara is awake for 100 hours a week. Show in a graph the budget line for Sara if she earns 6, 8 or 10 € per hour. Draw the indifference curve for Sara in a way in which her labor supply curve is positively sloped if the wage is between 6 and 8 € and negatively sloped if it is between 8 and 10 €.


20

Esercitazione n.7

100 Leisure time (hours)

Consumption(€)

600

800

1000

Sara’s budget line when she earns 10€ per hour, maximum consumption 1000€, maximum n° of hours of leisure time 100




21

Esercitazione n.7

Between 6€ and 8€ of hourly wage.

Indifference curves that result in a positively sloped labor supply curve (labor supply increases with the wage) must exhibit an increase in the worked hours, and therefore a reduction of leisure, after an increase in the wage.

Leisure is relatively more expensive, as the wage increases, and the substitution effect implies a reduction of leisure. The income effect determines an increase in the consumption of all goods, included leisure. In such case the substitution effect must prevail, with a net reduction of leisure, and a labor supply curve which is positively sloped.


22

Esercitazione n.7

Between 8€ and 10 € of hourly wage.

Indifference curves that result in a negatively sloped labor supply curve (labor supply decreases as the wage increases) must exhibit a reduction in worked hours, therefore an increase of leisure, as the wage increases.

Leisure is relatively more expensive, if the wage increases, and the substitution effect has the effect of reducing the hours of leisure and increasing the quantity of consumed goods. The income effect determines an increase in the consumption of all goods, included leisure.

In such a case the income effect must prevail, with a net increase of leisure, that brings to a negatively sloped labor supply curve.


23

Esercitazione n.7

For a wage between 6€ and 8€ leisure time reduces from L1 to L2. For a wage between 8€ and 10€ leisure time increases from L2 a L3

100 Leisure time (hours)

consump (€)

600

800

1000

L2 L1 L3

C1

C2

C3

The consumption of goods different from leisure always increases as the wage increases


24

Esercitazione n.7Practice ExerciseIn the labor market, when wages increase, the substitution effect determines an increase of the quantity of labor, while the income effect brings a reduction of the quantity of labor.

(True/False) Describe with a graph. True

Initial situation: point A

Hourly wage 50 €, 20 hours available for labor and leisure time

Choice of the worker, given his preferences: 6 hours of leisure and 14 hours of work at 50 € that allow a consumption of 700 €

After the wage increase: point B

Hourly wage 75 €, 20 hours available for labor and leisure time, the maximum availability of leisure does not change, but the maximum amount of consumption changes. For each hour devoted to leisure one abandons the possibility to consume a greater quantity of goods.

Worker’s choice, given his preferences: 5 hours of leisure and thus 15 hours of work that allow to consume goods for 1125 €


25

Esercitazione n.7

consump

Leisure time

I2

I3

I1

A

6 hours

700 €

C

5

hours

B1125 €


26

Esercitazione n.7

Substitution Effect: from A to C

The wage increase renders leisure more expensive in terms of consumption, therefore one increases consumption and reduces leisure, i.e. the worked hours increase

Income Effect: from C to B

The wage increase determines an income effect similar to an increase in the income, so both leisure and consumption of other goods increase, i.e. the worked hours decrease

esercitazione n.7 jose franchinoistituzioni di economia 2002/2003 corso c 1 chapter: 18 – the...

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