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Consider the production function q=aK + bL. a. Show that the cost-minimizing choice of K and...

Consider the production function q=aK + bL.

a. Show that the cost-minimizing choice of K and L may not be unique. (The cost-minimizing K and L levels are those used at a firm’s cost-minimizing point; the levels are not unique if there is more than one optimal combination of K and L for any one isoquant.)

b. Show on a diagram that, if the cost-minimizing choice of inputs is unique, it will generally entail the use of only K or only L. Under what conditions would the firm choose only K (and no L)? That is, what is the mathematical relationship between w/r and b/a when the firm chooses only K?

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