Question

Find the cost minimizing input combinations in the following problems: - f(k, ℓ) = 4k^3 ℓ^2...

Find the cost minimizing input combinations in the following problems:

- f(k, ℓ) = 4k^3 ℓ^2 , r = 2, w = 1, q = 100

- f(k, ℓ) = min{2k, 3ℓ}, r = 2, w = 3, q = 10

2. In the above question, you found the cost minimizing input combination that produces 100 units of output. Now find the cost minimizing input combination for any positive quantity of output q to obtain the firm’s conditional factor demand functions at the given input prices. Next, write down the firm’s cost function.

3. Suppose the firm is operating in the short run and cannot change its capital input, which is currently fixed at 64 units. In each case above, how many units of labor does the firm need in order to produce 100 units of output? Given that capital is fixed at 64 units, find the cost minimizing input combination that produces 100 units of output.

(a) Assuming again that capital is fixed at 64 units, find the cost minimizing input combination for any positive quantity of output q to obtain the firm’s short-run conditional factor demand functions at the given input prices. Next, write down the firm’s short-run cost function

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