Question #2445

Hi!
I have some problem with some micro problems. Could you help a little bit?
1. A firm has a production function given by f(x1,x2,x3,x4)=min{2x1+x2,x3+2x4}. What is the cost function for this technology? What is the conditional demand function for factors 1 and 2 as a function of factors prices (w1,w2,w3,w4) and output y?
2. Suppose that the firm has two possible activities to produce output. Activity a uses a1 units of good 1 and a2 units of good 2 to produce one unit of output.Activity b uses b1 units of good 1 and b2 units of good 2 to produce 1 unit of output. Factors can only be used in these fixed proportions. If the factor prices are (w1,w2), what are the demands for these two factors? What is the cost function for this technology? For what factor prices is the cost function not differentiable?
3. A firm uses 4 inputs to produce 1 output. The production function is
f(x1,x2,x3,x4)=min{x1,x2}+min{x3,x4}
What is the cost function?
If you could give some hints or examples that'd be great

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