# Micro doubts. Please help.

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## Micro doubts. Please help.

 Q1.A firm has the long- run cost function C(q)= 3q2+ 27. In the long run, it will supply a positive amount of output, so long as the price is greater than? Q2. If output is produced according to Q= 4LK,the price of K is \$10, and the price of L is \$5, then the co st minimizing combination of K and L capable of producing 2 units of output is? Q3. A firm uses a single input to produce its output, which is sold in a competitive market. It gets quantity discounts on purchases of its input. If it buys x units of the input, the price it must pay per unit of input is 289/x+ 3. If it buys no inputs, it doesn't have to pay anything. The firm's production function is f ( x) = 45x-x2. If the price of the firm's output is 1, the profit-maximizing amount of input to buy is? Please share how to solve these.
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## Re: Micro doubts. Please help.

 Assuming a perfect competition set-up, the quantity supplied in the long run will correspond to the minimised average total cost. i.e. q= 3 by profit maximization you get p=MC => p>6q so for price greater than 18 firm will supply non zero output
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## Re: Micro doubts. Please help.

 In reply to this post by MR Q3 profit= p*f(x) - cost per unit*x differentiate and put equal to zero x=21 second differential in negative...so need its the optimal point
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## Re: Micro doubts. Please help.

 In reply to this post by MI Hey MI, Thanks for replying. But how is the ATC 3? shouldn't it be 3q + 27/q?
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## Re: Micro doubts. Please help.

 minimize ATC, that happens at q=9
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## Re: Micro doubts. Please help.

 Oh ok. Thanks. Here is another question, let me know if you can solve it. A profit-maximizing competitive firm uses just one input, x. Its production function is q = 8x1/2. The price of output is \$24 and the factor price is \$8. The amount of the factor that the firm demands is?
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## Re: Micro doubts. Please help.

 It sqrt x.
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## Re: Micro doubts. Please help.

 In reply to this post by MR Calculate MRPL i.e = MPL *P and equate it to W. Which is 8 here.