Question

In: Economics

1. The following is a total-product schedule for a factor. Assume that the firm employs only...

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.

Expert Solution

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.

Rahul Sunny answered 1 year ago

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