part 1. Leave 'r' and 'w' as constants. Solve the cost minimization problem to find L*(q) and K*(q). Then find the cost function C(q).
part 2. At what price would the firm choose to shutdown and not produce? Provide calculations.
![**10:** Consider a car manufacturer which uses capital \( K \) and labor \( L \) to produce \( q \) cars according to the production function
\[
q = f(L, K) = L^{\frac{1}{8}} K^{\frac{3}{8}}
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"Since you have asked multiple parts, we will answer only the first part for you. If you have any other doubt, then mention it ore repost the question."
The Production function of a car manufacturer is given as:
Where q is the cars produced by the manufacturer using the "K" capital and "L" labour. The cost function of the manufacturer is the cost of inputs firm has to pay like wages (w) of labourers and rent (r) of the capital.
Now, the cost function should be:
Where L* and K* are the optimal cost minimization level of inputs.
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