The short-run cost function of a company is given by the equation TC = 200 + 55q, where TC is the total cost and q is the total quantity of output, both measured in thousands.

1. What is the company's fixed cost?

2. If the company produced 100,000 units of goods, what would be its average variable cost?

3. What would be its marginal cost of production?

4. What would be its average fixed cost?

5. Suppose the company borrows money and expands its factory. Its fixed cost rises by \(50,000, but its variable cost falls to \)45,000 per 1000 units. The cost of interest (i) also enters into the equation. Each 1-point increase in the interest rate raises costs by $3000. Write the new cost equation.

TC = 200 + 55q (in thousands)

The fixed cost is independent of the output quantity. Therefore, the fixed cost for the given short-run cost function is $200,000.

Step 3: The marginal cost of the productionFrom the given cost function, the variable cost is 55q.

Thus the average variable cost for 100,000 units is $55,000 (= 55q/q in thousands).

The marginal cost is the change in total cost by an additional unit of output.It is calculated as:

$$\begin{gathered} MC=\frac{dTC}{dq} \\ =\frac{d\left(200+55q\right)}{dq} \\ =55 \end{gathered}$$

Thus, the marginal cost of production is $55,000.

The fixed cost of production is $200,000, as given in the total cost function.

The average fixed cost is calculated as:

$$\begin{gathered} \mathit{A}\mathit{F}\mathit{C}\mathbf{=}\frac{\mathbf{F}\mathbf{C}}{\mathbf{q}} \\ =\frac{200,000}{100,000}=2 \end{gathered}$$

Thus, the average fixed cost for 100,000 units is 2.

The fixed cost increases by $50,000. Thus, the new fixed cost will be $250 (in thousands). The variable cost per 1000 output has declined to $45 (in thousands). Also, the interest rate has come into play for determining the variable cost. For each 1% increase in interest rate (i), income increases by $3 (in thousands).So, the variable cost will depend on output and interest rate.

Hence, the new total cost function is:TC = 250 + 45q + 3i