Suppose that a firm’s fixed proportion production function is given by:
q = min{5k, 10l}
Please calculate the firm’s long-run total, average, and marginal cost functions.
Given
Production function is given as
q = min{5k,10l}
calculation of long run total cost
Total Cost is minimized where "5K=10l"
"k=2l" or "l=\\frac{k}{2}"
Now we got the value of k put it in production function
q=min{5k,5k}
q=5k
"k=\\frac{q}{5}"
Now put "k=\\frac{q}{5}" in total cost function
"l=\\frac{k}{2}"
"l=\\frac{q}{\\frac{5}{2}}"
"l=\\frac{q}{10}"
therefore Total Cost function is TC = w*l + r*k
put the values of l and k
TC = "w*\\frac{q}{10}+r*\\frac{q}{5}"
Calculation of average Cost
"AC=\\frac{TC}{q}"
where, TC = "w*\\frac{q}{10}+r*\\frac{q}{5}"
"AC=\\frac{w}{10}+\\frac{r}{5}"
Calculation of Marginal Cost
MC ="\\frac{\\delta TC}{\\delta q}"
where TC = "w*\\frac{q}{10}+r*\\frac{q}{5}"
MC = "\\frac{w}{10}+\\frac{r}{10}"
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