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Unformatted text preview: ECMC41- WEEK #1 (Ch2) – SOLUTIONS Textbook questions Ch2 : 1, 3, 5 & 7 – Solutions to odd numbered textbook problems appear at the end of the book. Q1. Distinguish between returns to a variable factor of production (input), and returns to scale. Returns to a (single) variable factor of production (or input) can be described using either of two popular measures the average productivity of the input OR the marginal productivity of the input. These measures assume that only a single (variable) input is varied (i.e. all other inputs are held fixed). For example, suppose we are speaking of the variable labour input we might look at the marginal productivity of labour (MP L ) or the average productivity of labour (AP L ). Where these are defined as follows: L Y MP L ∂ ∂ = = the change in output (Y) as we change L at the margin L Y AP L = = the average amount of output made per worker employed Returns to scale refers to a slightly different thought experiment. It measures the amount of output created (returned) as we scale the use of all inputs up (or down) by the same scale factor (i.e. all inputs are varied and by the same scale factor or percentage – perhaps by a discrete rather than a marginal amount). ) , ( K L F Y x ⋅ ⋅ = ⋅ λ λ λ , where Y = output K = capital input employment level L = labour input employment level F( ) = production function λ = scale factor > 0 x = 1, implies Constant Returns to Scale (CRTS) x > 1, implies Increasing Returns to Scale (IRTS) x < 1, implies Decreasing Returns to Scale (DRTS) 1 | P a g e Note: A particular production function (technology) might exhibit CRTS, IRTS, or DRTS over all levels of input use (i.e. for all scale factors λ). While some productions functions could exhibit CRTS over a subset of the set of possible inputs usable, IRTS over another region and perhaps DRTS over another region of inputs. So both concepts are related since they measure the return (in terms of units of output returned) as we vary the use of inputs they each speak to slightly different experiments – one definition/experiment assumes we only vary a single input while the other assumes we vary all inputs (by the same scale factor or percentage). Q2. Explain why a firm’s short-run average cost function may be U- shaped. Explain why a firm’s long-run average cost function may be U-shaped. Suppose our firm’s production function is given as follows: Y = F(K,L), where Y is the level of output produced, K is the level of capital used & L is the level of labour input used. Short-run production and costs In the short-run the level of capital employed is assumed to be fixed (K =K ) as is the technology we use to produce output. Thus output can be varied solely by varying the level of labour employed (used). Of course in the short-run if the firm wants to produce a particular level of output (Y SR ) it will set its level of employment of workers to minimize cost....
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- Summer '10
- Economics of production, APL