a watch making firm operating in a competitive market.given by c= 100+ q2., where q is the level of output & c is total cost.
a.the price of watches is birr is 60, how many watches produce to maximize profit?
b.what will your profit level be?
c.at what minimum price will you produce a positive output?
Suppose the fixed costs at a widget factory are $500.00 and variable costs per widget are as indicated. Compute the total average costs for each of the following:
Producing 10 widgets when the variable cost is $10 per widget
Total Cost = $ __100_______
Average Cost = $ _________
Producing 20 widgets when the variable cost is $15 per widget
Total Cost = $ _________
Average Cost = $ _________
Producing 100 widgets when the variable cost is $20 per widget
Total Cost = $ _________
Average Cost = $ _________
sove this
To find the optimal level of output that maximizes profit, you need to determine where the marginal cost (MC) equals the price (P). In this case, the price (P) is given as 60 Birr and the total cost (C) function is given as C = 100 + q^2, where q is the level of output.
a. To find the optimal level of output, you need to find where MC = P. The marginal cost can be found by taking the derivative of the total cost function with respect to q. So, let's calculate MC:
MC = dC/dq
To find the derivative, take the derivative of each term separately:
dC/dq = d/dq (100 + q^2)
= 0 + 2q
= 2q
Now set MC equal to the given price (P):
2q = 60
Therefore, q = 30.
So, to maximize profit, the firm should produce 30 watches.
b. To calculate the profit level, we need to subtract the cost (C) from the revenue (R). Revenue (R) can be calculated as the product of the price (P) and the quantity (q).
R = P * q
= 60 * 30
= 1800 Birr (revenue)
Now, let's calculate the cost (C):
C = 100 + q^2
= 100 + 30^2
= 100 + 900
= 1000 Birr (cost)
Profit (π) can be calculated as follows:
π = R - C
= 1800 - 1000
= 800 Birr
Therefore, the profit level will be 800 Birr.
c. To find the minimum price at which the firm will produce a positive output, set the cost (C) equal to zero and solve for the quantity (q).
C = 100 + q^2
Since we want to find the minimum price at which the firm will produce a positive output, we need to find the smallest positive value of q when C = 0.
0 = 100 + q^2
Solving for q will give us the minimum value of q at which the firm will produce a positive output. However, in this case, the given cost function does not have a solution where C = 0 and q > 0. Therefore, we cannot determine the minimum price at which the firm will produce a positive output with the given cost function.