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Problem_Set__4_-_Production_Functions - 5 How does cost...

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Econ 701 – Microeconomic Theory - Problem Set #4 Production and Cost functions Consider the following production functions (all greek letters are parameters): a. α α - = 1 l k q b. ) ln( ) 1 ( ) ln( l k q α α - + = c. ] , min[ l k q β α = d. α α δ - - = 1 ) ( l k q 2. For each of the above functions, find an expression for the Marginal Rate of Technical Substitution (where possible), and sketch the isoquants. Be sure to clearly label axes and intercepts. 3. In utility theory, we saw that functions like b) and a) were effectively identical. Is this true for production functions? Do these functions have the same “scale” properties? That is, do both a) and b) exhibit constant returns to scale? Now, consider the production function: 3 1 3 1 l Ak q = . 4. Find the cost function associated with this production function.
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Unformatted text preview: 5. How does cost change with output, and what is true about the returns to scale in the above production function? 6. Suppose now that k is fixed at some level k in the short run. Find the short run cost function associated with the above production function. There should be some fixed costs in your production function…where do these come from? 7. On the same graph, plot the short run cost function and the long run cost function. At what point do these functions cross or intersect? Hint: don’t be afraid to look at Figure 8.8 and surrounding material for guidance. Repeat problems 6-9 for the production function ) ( 2 1 2 1 l k A q + = ....
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