3. (24 points) Suppose a competitive firm can sell its output for $5 per unit. T

Question

3. (24 points) Suppose a competitive firm can sell its output for $5 per unit. The following table gives the firm’s short run production function.

Labor Output
0 0
1 60
2 130
3 180
4 220
5 250
6 260

In the table below, you will determine several points on the firm’s demand curve for labor. To do this, you must determine how many workers the firm should hire for different values of the wage rate in order to maximize profit. Complete the table below:


Wage Rate Per Worker Quantity Demanded of Workers
$45 ?
$75
$225
$270
$320
$340

Explanation / Answer

Labor Output Marginal Product Price MRP 0 0 $5 1 60 60 5 $300 2 130 70 5 350 3 180 50 5 250 4 220 40 5 200 5 250 30 5 150 6 260 10 5 50 Marginal Product: additional output per each labor unit. Price is price of output. MRP is the marginal revenue product of labor which is calculated by multiplying MP with Price MRP = MPx Price MRP at 6th unit = 10 x $5                         = $50 For a competetive firm, profit maximizing resource allocation takes place when MRP equals to wage rate. MRP = wage rate. that is additional revenue generated should equal to the market wage rate. Thus when wage rate is $45 which is lower than the MRP at 6th unit of labor. It is profitable to hire 6 workers. i.e the 6th unit of labor costs the firm $45 and this 6th additional unit will bring in marginal revenue of $50, so it is profitable to hire 6 units of labor(workers) wage rate $75: $75 is higher than the MRP of $50 but lower than the MRP of $150 so we can hire 5 workers comfortably. Wage Rate Quantity demanded $45 6 workers $75 5 $225 3 $270 2 $320 2 $340 2 Labor Output Marginal Product Price MRP 0 0 $5 1 60 60 5 $300 2 130 70 5 350 3 180 50 5 250 4 220 40 5 200 5 250 30 5 150 6 260 10 5 50

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