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Question: properties of the cobbdouglas production func tion suppose iphones are...

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Properties of the Cobb-Douglas Production Func- tion Suppose iPhones are produced using three input factors combined in a Cobb- Douglas production function where K is capital and Lu and Ls are unskilled and skilled labour. 1. What assumptions on a, b, and c must be true for this production function 2. Given your answer in part a), explain why this production function ex- 3. Now assume a + c 1, and b 0 (i.e. no unskilled labour is used in to exhibit constant returns to scale? hibits diminishing returns to any single factor (Hint: use derivatives) production). Derive the relative factor demand function ()) under the standard Heckscher-Ohlin assamptions where K/L is a function of w/r and a. 4. Define the cost share of each factor (share of the total cost of each factor) as cK = umrR and CL = ul+rR: Using the assumption and your result from 3., show that these cost shares are a function of a. Are they also a function of relative factor prices? 5. Now suppose iPhones take some n number of input factors to manufacture. The production function now takes the following form: (a) What assumption on the as must be true for this production to exhibit increasing returns to scale (i.e. increasing each input by some amount results in an increase in the output by a greater factor). Prove it using the production function.
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