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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