The short-run cost function of a firm is as follows:

TC = 200 + 5Q + 2Q2
Where TC = Total Cost
Q = Physical units of the product of the firm
What would be the level of optimum output?

Tc=40,000+300Q2-Q3

student

10

I want answers

1. Suppose the short run cost function of a firm is given by: TC=2Q3-2Q2+Q+10

2

To find the level of optimum output, we need to determine the quantity at which the cost is minimized. In other words, we have to find the point where the cost function is at its lowest.

To do this, we can take the derivative of the cost function with respect to Q and then set it equal to zero. This is because at the point where the derivative is zero, we have reached a minimum (or maximum) point on the cost function.

Let's find the derivative of the cost function:

TC = 200 + 5Q + 2Q²

To take the derivative, we treat Q as the variable and differentiate each term separately:

dTC/dQ = d(200)/dQ + d(5Q)/dQ + d(2Q²)/dQ

Since the derivative of a constant term (like 200) is zero, and the derivative of Q with respect to Q is 1, we can simplify the expression:

dTC/dQ = 0 + 5 + 2(2Q)

Simplifying further:

dTC/dQ = 5 + 4Q

Now we set the derivative equal to zero and solve for Q:

5 + 4Q = 0

Rearranging the equation:

4Q = -5
Q = -5/4

However, since Q represents the physical units of the product, it cannot be negative. Thus, we discard the negative solution.

Therefore, the level of optimum output (Q) for the firm is 0.

This means that the firm should not produce any units of the product in order to minimize its costs in the short run.

Suppose the firm faces a demand curve for its product P=32-2q

And the firms costs of product
And marketing are C(q)
Find the following
A) the formula for profit in terms of Q
B) the maximum total revenue to be generated
C) the price and quantity that minimize total revenue and the correspondening value of total revenue.

Q=10p-3 and TC=2Q