380 Problem Set _8-technology

# 380 Problem Set _8-technology - Problem Set 8-Chapter 9...

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Problem Set 8-Chapter 9 Technology Econ 380 R. Pope W2011 Less Technical 1. For constant returns to scale technology, the marginal product of labor only depends on the ratio of capital to labor. Would less or more capital per worker lead to a larger marginal product of labor? (I will accept an answer that uses a specific functional form like the Cobb-Douglas 1 q Ak l α α - = ) 2. If there is neutral technical change, the production function is ( ) ( , ) q f t h k l = where t represents time and technical change. Does technical change affect the marginal rate of substitution between capital and labor? 3. If an economic planner, has 1000 tons of fertilizer to allocate to wheat production in two regions, what rule should the planner use to allocate the fertilizer if total output of wheat is to be maximized. In the end, where would the rule lead? (Hint: this is an example of the equi-marginal rule. Set up the Lagrangian and solve if you can’t reason intuitively).
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