Question: Orla manages a loom that produces flags (F) using thread (T) and dye (D) as inputs. Her production function is given by: Q(T,D) = (T1/2 D1/2)1/2 *For this problem, assume F, T, and D are infinitely divisible so you don’t need to worry about restricting to whole-number answers. a.) Does Orla’s production function exhibit increasing, constant, or decreasing returns to scale? Explain. b.) Set up Orla’s cost-minimization problem to find the lowest-cost combination of inputs required to produce a specific level of output (bar Q) given factor prices PT and PD. (Note: You can write this either as a minimization subject to constraints or in Lagrangian form. *You do not need to solve it.)
Question: Orla manages a loom that produces flags (F) using thread (T) and dye (D) as inputs. Her production function is given by: Q(T,D) = (T1/2 D1/2)1/2 *For this problem, assume F, T, and D are infinitely divisible so you don’t need to worry about restricting to whole-number answers. a.) Does Orla’s production function exhibit increasing, constant, or decreasing returns to scale? Explain. b.) Set up Orla’s cost-minimization problem to find the lowest-cost combination of inputs required to produce a specific level of output (bar Q) given factor prices PT and PD. (Note: You can write this either as a minimization subject to constraints or in Lagrangian form. *You do not need to solve it.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question: Orla manages a loom that produces flags (F) using thread (T) and dye (D) as inputs. Her
production function is given by: Q(T,D) = (T1/2 D1/2)1/2
*For this problem, assume F, T, and D are infinitely divisible so you don’t need to worry
about restricting to whole-number answers.
a.) Does Orla’s production function exhibit increasing, constant, or decreasing returns to
scale? Explain.
b.) Set up Orla’s cost-minimization problem to find the lowest-cost combination of inputs
required to produce a specific level of output (bar Q) given factor prices PT and PD. (Note: You can write this either as a minimization subject to constraints or in Lagrangian form. *You do not need to solve it.)
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