The current market wage rate is $10, the rental rate of land is $1,000 per unit, and the rental rate of capital is $500. Production managers at a firm find that under their current allocation of factors of production, the marginal revenue product of labor is 100, the marginal revenue product of land is $10,000, and the marginal revenue product of capital is $4,000. Is the firm maximizing profit?
Maximizing profits? No. For any given level of capital (or land, or anything else), the Marginal Revenue Product of Labor must be equal to its Marginal Cost (or the wage rate if we assume the labor market is competitive).
Given the numbers above, $100 > $10 (this basically says the next worker brings in $100 to the firm, but only costs them $10). They could still hire more workers at $10, and have them bring in more money (although the $100 would drop for each new worker due to diminishing returns). It falls all the way down to 10 (when 10 = 10) and you won't hire anymore workers (because the next worker would cost you $10, but he would bring in something lower than $10... why hire him then?).
To determine whether the firm is maximizing profit, we need to compare the marginal revenue products (MRP) of each factor of production to their respective prices.
In this case, the MRP of labor is $100, which is greater than the wage rate of $10. Therefore, the firm is willing to pay more for an additional unit of labor than its current price. This suggests that the firm could increase its profits by employing more labor.
In contrast, the MRP of land is $10,000, which exceeds the rental rate of $1,000 per unit. This indicates that the firm is already paying more for land than its marginal contribution to revenue. Therefore, the firm should not increase its use of land as it would result in diminishing returns and reduced profits.
Similarly, the MRP of capital is $4,000, while the rental rate is $500. This implies that the firm should use more capital since the marginal revenue generated by an additional unit of capital is higher than its rental cost.
Based on these calculations, the firm is not maximizing profit because it should increase its use of labor and capital while decreasing its use of land to reach an optimal allocation of factors of production.