Answer to Question #270136 in Microeconomics for Camila

Question #270136

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.


1
Expert's answer
2021-11-23T09:05:25-0500

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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