Question

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Principles of Microeconomics-Assignment No. 3 Use the following table to determine the optimal input usage of labor. Labor can be hired for S14 per hour (there are no other costs involved in employing labor). Labor Qty/hr. 10 Price $18.00 8.69 6.25 5.40 5.06 4.85 4.75 4.70 If the firm sells its output in a competitive output market for $5 per unit (ignore the Price column for this question), then how many workers should be employed in order to maximize profits? If the employees of the firm now unionize and negotiate a wage of $26 per hour, then how many workers should now be employed in order to maximize profits? (The output price is still $5 per unit.) Assume, once again, that the wage is $14 per hour. Also assume that the firm is now a monopolist (use the Price column for this question). How many workers should be employed by the monopolist in order to maximize profits?

Answer 1

1.

Given: Price = $5 per unit & wage = $14 per hour

Value of Marginal Product of labour(VMPL) = P x MPL

Labour	Output	MPL	VMPL
0	0	0	-
1	10	10	50
2	25	15	75
3	37	12	60
4	45	8	40
5	50	5	25
6	54	4	20
7	56	2	10
8	57	1	5

The perfectly competitive firm reaches its equilibrium and maximises profit when:

VMPL = w

We see that for the 7th worker, VMPL($10) < Wage($14).So, we'll hire only 6 workers.

2.

Now, if employees negotiate a wage of $26 per hour, from the above table we can see that for the 5th worker,

VMPL($25) < Wage($26), so we'll hire only 4 workers.

3.

We know that,

Total Revenue(TR) = Price x Quantity

Marginal Revenue(MR) = TRn -TRn-1

Marginal Revenue Product(MRP) = MPL x MR

Labour	Output	MPL	Price	TR	MR	MRP
0	0	-	0	-	-	-
1	10	10	$18.00	$180	180	1800
2	25	15	8.69	217.25	37.25	558.75
3	37	12	6.25	231.25	14	168
4	45	8	5.40	243	11.75	94
5	50	5	5.06	253	10	50
6	54	4	4.85	261.9	8.9	35.6
7	56	2	4.75	266	4.1	8.2
8	57	1	4.70	267.9	1.9	1.9

The monopolist firm, being a profit maximiser, will be in equilibrium when :
MRPL = w

The wage is $14 per hour. For the 7th worker, we see that MPL(8.2) < w(14) so, the firm will hire only 6 workers.