2 questions that im stuck on!!!

1. Suppose a firm has a production function Q = 3(squareroot)N, where N is labour.
Suppose the wage is 3, and the price of the output 4.
(a) Write the Firm profits

(b) Calculate the firm optimal labour choice when the wage is 3.

2. 2. Suppose a fim has a production function Q = 3(squareroot)N, where N is labour.
Suppose the price of the output 4. Derive the firm labour demand

a) I suggest you create a table. Columns are N, Q, Total Revenue, and Profit. Rows are N=1,N=2,...N=5. That is, calculate Q, Total Revenue, and profit when wage=3*N and when N=1, when N=2 and so on. Where is profit maximized?

b) use the table you created in a) How much would the firm pay per worker if it only wanted 1 worker, if it wanted 2 workers, ... if it wanted 5 workers.

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1. (a) To calculate the firm's profits, we need to subtract the total cost from the total revenue. The total revenue can be calculated by multiplying the price of the output by the quantity produced:

Total Revenue = Price of output × Quantity
Total Revenue = 4 × Q

Total cost is the product of the wage and the quantity of labor used:

Total Cost = Wage × Labor
Total Cost = 3 × N

Profit is obtained by subtracting the total cost from the total revenue:

Profit = Total Revenue - Total Cost
Profit = 4 × Q - 3 × N

(b) To find the firm's optimal labor choice, we need to maximize the profit function with respect to labor (N). Differentiate the profit function with respect to N and set it equal to zero to find the critical point, then solve for N.

2. (a) To derive the firm's labor demand, we need to determine the level of labor (N) that maximizes the profit. We can do this by calculating the profit for different levels of labor and finding the one that yields the highest profit.

You can create a table to help with calculations. The columns of the table will be N, Q, Total Revenue, and Profit. The rows will represent different levels of labor (N = 1, 2, 3, ..., 5). Calculate Q (the quantity produced) using the given production function Q = 3√N. Then, calculate the total revenue by multiplying the price of output (4) with the quantity Q. Finally, calculate the profit by subtracting the total cost (wage × labor) from the total revenue.

For each level of labor, fill in the table, calculating Q, Total Revenue, and Profit. Analyze the table to determine at which level of labor the profit is maximized.

(b) Once you have the table from (a), you can determine how much the firm would pay per worker for different levels of labor. To do this, divide the total cost (wage × labor) by the quantity of labor used (N). Fill in the table with these calculations for each level of labor.

This will provide you with information on how much the firm would pay per worker for a given number of workers.