Suppose that the price per unit of input C is 10 euros and the price per unit of input K is 8 euros. What is the minimum cost of producing 40 units of output Y for the firm if the firm’s production function is Y = min {C/2 ; 4K}, where Y denotes the quantity of output Y produced, C denotes the quantity of input C used and K denotes the quantity of input K used? (10 points)
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It is 200. It is because the minimum value of the inserted items in the bracket has to be taken. In this case, there is C/2 and 4K, where C is 10 and K is 8.
Therefore, C/2 comes to 5 whereas, 4K becomes 32. Hence, we have to consider C/2, i.e., 5. the minimum cost of producing 40 units of the same will be 200.
Hence, 200 is the correct answer according to me. Unless min{x,y} does not mean something else, it can be true for all values.
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