Determine the profit maximizing output for a firm exhibiting the following:
Demand Schedule: P = 4000 – 33Q
TC = 2Q3 – 3Q2 + 400 + 5000
*Be sure to check the second order conditions to assure your solution is valid.
2. Suppose a firm exhibits the following cost function:
TC = Q3 – 5Q2 + 60Q
a. Is this firm operating in the long run or short run? How do you know?
b. Find the level of output at which this would operate at minimum efficient scale.
3. Given the following production function;
Q = 10K 0.7 L 0.1, where PK = 28 and PL = 10 and C = 4000
a. Does this production function exhibit diminishing returns in both capital and labor? How do you know?
b. Does this production function exhibit increasing, decreasing, or constant returns to scale? How do you know?
c. Find the optimal levels of capital and labor that will maximize output.
4. Given the following short run production function:
Q = 7.5L2 – 0.5L3
a. The level of labor at which diminishing returns begins.
b. The levels of labor at which stage II production begins and ends.
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