4I Production and Costs

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Gustavo Indart

PRODUCTION AND COSTS The Production Function Q = f(L, K) Q = flow of output, L = flow of labour services, K = flow of capital services, changes in technology = changes in f Profit-Maximizing Output profit = TR - TC TR = total revenue, TC = total cost Total, Average, and Marginal Products Total Product (TP or q): total amount produced by a firm during same time period Average Product (AP): AP = TP/L Marginal Product (MP): MP = dTP/dL Law of diminishing returns: if increasing quantities of a variable factor are applied to a given quantity of fixed factors, the variable factor’s marginal product will eventually decrease Where AP reaches its maximum, MP = AP The average curve slopes upward as long as the marginal curve is above it. For example, if MP > AP, AP is rising, if MP < AP, AP is falling. Short-Run Costs Explicit Costs: costs of purchasing/hiring inputs from firms/households Implicit Costs: opportunity costs of inputs owned by the firm itself that are not explicitly paid Total Cost (TC): TFC + TVC Total Fixed Cost (TFC): all costs of production that do not vary with level of output Total Variable Cost (TVC): total costs of production that vary directly with level of output Average Total Cost (ATC): ATC = TC/Q or ATC = AFC + AVC Average Fixed Cost (AFC): TFC/Q Average Variable Cost (AVC): TVC/Q Marginal Cost (MC): MC = dTC/dQ = w/MP (MC = competitive firm’s supply curve) AVC and MC curves are both U-shaped because : Eventually diminishing AP of the variable factor implies eventually increasing AVC. Eventually diminishing MP of the variable factor implies eventually increasing MC. ATC curve is U-shaped because it only begins to rise when the effect of the increasing AVC dominates the effect of the declining AFC. NOTE: Min AVC = MC Change in Fixed Costs TC = TCo + ∆FC 1 1) MC 1 ∆(TCo + ∆FC)/∆q = ∆TCo/∆q = MCo - No change in MC - No change in AVC 2) AFC = (FCo + ∆FC)/q = AFCo + = ∆FCq 1 - Nonparallel shift in AFC 3) AC = (TCo + ∆FC)/q = ACo + ∆FC/q 1 - Nonparallel shift in AC Change in Variable Costs TC 1 TCo + ∆VC*q 1) MC 1 ∆(TCo + ∆VC*q)/∆q = ∆TCo/∆q + ∆VC*q/∆q = MCo + ∆VC - Vertical (parallel) shift in MC by ∆VC - Vertical (parallel shift in AVC 2) No change in Fixed Costs (since Variable Costs do not affect Fixed Costs) 3) AC 1 (TCo + ∆VC/q)/q = ACo + ∆VC - Vertical (parallel shift in the AVC Long-Run Co
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