if the marginal product of capital of a firm is 120unit of output, rental price of machine is $30. and marginal product of labor is 40units of output, daily wages is $20.
1)why is this firm not maximizing output or minimizing cost in long run??
2)how can the firm max. output or min. cost?
The firm could fire one worker -- production goes down by 40 and use the savings to buy $20 worth of capital -- output goes up by 80, for an overall net gain of 40.
Profit is maximized when MPk/Pk=MPl/Pl
(MP - is marginal product, P is the input price)
ttr
To determine whether the firm is maximizing output or minimizing cost in the long run, we need to evaluate the marginal cost of production and compare it to the market price. Here's how we can calculate both:
1) To determine whether the firm is maximizing output, we need to compare the marginal cost of production (MC) to the market price. The firm is not maximizing output if MC is less than the market price. If MC is greater than the market price, it means the firm is producing at a higher cost than what they can sell it for in the market. In this scenario, let's say the market price is $40 per unit.
To calculate the marginal cost (MC), we sum up the cost of labor (W) and the cost of capital (R) and divide it by the marginal product of labor (MPL). The formula is MC = (W / MPL) + (R / MPK), where MPL is the marginal product of labor and MPK is the marginal product of capital.
In this case, MPL is 40 units of output, W is $20 for daily wages, MPK is 120 units of output, and R is $30 for the rental price of the machine. Plugging in these values, we get:
MC = ($20 / 40) + ($30 / 120) = $0.50 + $0.25 = $0.75 per unit of output.
Since the market price is $40 and the marginal cost is $0.75 per unit, the firm is maximizing output since MC is less than the market price.
2) To maximize output or minimize cost, the firm should continue producing as long as the marginal cost of production (MC) is less than the market price. However, if MC exceeds the market price, the firm should reduce its output level to minimize costs.
Additionally, the firm can also consider adjusting its inputs to achieve cost-minimization or output maximization. They can analyze the marginal productivity of capital and labor and adjust their usage accordingly. If the marginal product per dollar spent on labor is higher than the marginal product per dollar spent on capital, the firm should employ more labor and vice versa. This allows the firm to efficiently allocate its resources and optimize its output and cost levels.
Overall, by continuously monitoring the market price and the marginal cost of production and adjusting input usage accordingly, the firm can maximize its output or minimize its costs in the long run.