Draw the isoquant for an output level

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Reference no: EM1374618

Consider a company that uses two inputs. The quantity used of input one is denoted by x_1 and quantity used of input 2 is denoted by x_2. The company produces and sells one good using the production function f(x_1,x_2)=4x_1^0.5+3x_2^0.5. The final good is sold at price P=$10. The prices of inputs 1 and 2 are w_1=$2 and w_2=$3, respectively. The markets for the final good and both input goods are treated as competitive markets by the firm, that is, it takes prices as given.

a) Demonstrate whether the production function has increasing, decreasing, or constant returns to scale.

b) Make the isoquant for an output level of 12. Clearly label the axes and the curve and show any two input bundles on the curve by indicating their coordinates.

Now consider the long run, where the quantity of input 2 can be varied.

c) According to your answer in part a), does the firm have a profit maximising plan in the long run? If no, explain why. If yes, is the plan unique?

d) Write down the firm's profit function and the firm's long run profit maximisation problem. Find the firm's optimal use of input 1, input 2, the associated optimal quantity of the output, and the firm's profit level.

Reference no: EM1374618

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