Jack & Jill Well Drilling, LLC is a company that drills water wells. The firm uses 2 inputs; labor (L) that costs $25 per unit and capital (K) that costs $100 per unit. The company's production function is given by (Q is drilling depth in hundreds of feet, Q = 2 means 200 feet)):
Q = L ^ 3/4 K^1/4
a. Write out the expression for the isoquant for 400 feet of drilling (remember Q is drilling depth in hundreds of feet).
a. If Jack & Jill intend to drill 400 feet of well and they have 4 workers hired, how many units of capital will they have to hire?
Suppose Jack & Jill have 4 permanent employees (long-run choice with contracts for these workers over the next 5 years). What are the short-run AVC and ATC functions? Hint: Costs are a function of the level of output produced so your functions should be in terms of Q, not K and/or L. That is, in general, what is the average variable and average total cost for any arbitrary level of output Q (hence, the functions should only involve Q)?
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