In: Economics
1. The following is a total-product schedule for a factor. Assume that the firm employs only one factor for production of the output.
Units of factor 1 2 3 4 5 6 7
Total product 24 42 54 64 72 78 82
a. If the product the firm produces sells for a constant $2 per unit, what is the marginal revenue product of the third unit of the factor?
b. If the firm's product sells for a constant $2 and the price of the factor is $16 per unit employed, how many units of the factor will the firm employ?
c. Based on the above question #b, what is this firm’s profit?
d. If the output price is increased to $3.00 per unit, how many units of the factor will this firm employ? Assume that the price of the factor is $16 per unit employed.
e. Based on the above question #d, what is this firm’s profit?
f. With the examples above, explain the relationship between the labor demand and the output price.
Marginal product (MP) = Change in Total product (TP) / Change in Factor (L)
L | Q | MP |
1 | 24 | |
2 | 42 | 18 |
3 | 54 | 12 |
4 | 64 | 10 |
5 | 72 | 8 |
6 | 78 | 6 |
7 | 82 | 4 |
(a) Marginal revenue product (MRP) = MP x Output price = 12 x $2 = $24
(b) Input demand is optimal when MRP = Wage Rate = $16.
When Output price = $2,
MP x $2 = $16
MP = 8
This holds true when 5 units of factor are used (with output = 72).
(c) Profit = Revenue - Cost = (Price x Q) - (Wage rate x L) = ($2 x 72) - ($16 x 5) = $144 - $80 = $64
(d) Input demand is optimal when MRP = Wage Rate = $16.
When Output price = $3,
MP x $3 = $16
MP = 5.33
When L = 6, MRP = $3 x 6 = $18 > Wage rate
When L = 7, MRP = $3 x 4 = $12 < Wage rate
Therefore, 6 units of factor will be used (with output = 78).
(e) Profit = Revenue - Cost = (Price x Q) - (Wage rate x L) = ($3 x 78) - ($16 x 6) = $234 - $96 = $138
(f) When Price = $2, L = 5 and when Price = $3, L = 6. Therefore, the higher (lower) the output price, the higher (lower) the demand for labor.