A firm’s production function is given by q = min{M, L1/2}, where M is the number of machines and L is the amount of labor that it uses. The price of labor is $1and the price of machines is $2 per unit.   a. Is this technology decreasing return to scale? Show your argument. b. Is it true the statement that if average production cost is increasing, a firm’s technology exhibits the decreasing return to scale. (If yes, show the proof. If not, show a counter example) c. Is it true that if a firm’s technology exhibits the decreasing return to scale, then average production cost is increasing? (If yes, show the proof. If not, show a counter example)

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Isocost and Isoprofit Curve Analysis

An isocost curve in the production theory that is a crucial part of economics depicts different combinations of factor inputs at a given market cost. In other words, this shows all the combinations of production factors that cost the same for the firm to employ. Usually, this can be depicted as a downward sloping straight line when the firms act as the price-takers in the factor markets. The slope of this mainly depicts the relative prices of different production factors.