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Homework answers / question archive / Please show steps to resolve these problems please use Lagrangian Multiplier if possible

Please show steps to resolve these problems please use Lagrangian Multiplier if possible. A manufacturer has the following production function: Q=100 K^{. 2} L^{. 9}

If the price per unit of labor is $20 and the price per unit of capital is $10,

- What is the optimal combination of labor and capital to use in order to maximize output for a total cost of $2,200?
- How much output will be produced?
- What is the equation for the expansion path?
- What is the meaning and value of λ (lambda)?
- What is the value of the marginal rate of technical substitution for labor and capital at the optimal point?
- Is there diminishing marginal productivity for labor and capital? Explain
- Are there increasing returns to scale? Explain

2 Given the following short–run production function, Q = 1500L + 60L^{2} – L^{3}

where Q is output and L is variable input, find

- The point of diminishing marginal returns.
- The point where the elasticity of production is equal to one.
- The boundary between stage II and stage III.
- Show that marginal product is equal to average product when average product is at its maximum.

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