8. Costs and Cost MinimizationCostsMeasuring (ALL) CostsMeasuring (ALL) CostsSlide Number 5Slide Number 6Slide Number 7Measuring (ALL) CostsSlide Number 9Slide Number 10Slide Number 11Short-Run CostsShort-Run Cost CurvesShort-Run CostsShort-Run Cost CurvesProduction Functions and the Shape of Cost CurvesProduction Functions and the Shape of Cost CurvesProduction Functions and the Shape of Cost CurvesEffects of Taxes on CostsShort-Run Cost SummaryLong-Run CostsLong-Run Costs and Input ChoiceIsocost LinesCost MinimizationCost MinimizationCost MinimizationCost Minimization with CalculusSlide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Output Maximization with CalculusOutput MaximizationFactor Price ChangesHow LR Cost Varies with OutputHow LR Cost Varies with OutputThe Shape of LR Cost CurvesLower Costs in the Long Run8. Costs and Cost Minimization • Measuring Costs • Short-Run Costs • Long-Run Costs • Cost Minimization • Conditional Input Demand Function and Cost Function 1Costs • How does a firm determine how to produce a certain amount of output efficiently? • First, determine which production processes are technologically efficient. • Produce the desired level of output with the least inputs. • Second, select the technologically efficient production process that is also economically efficient. • Minimize the cost of producing a specified amount of output. • Because any profit-maximizing firm minimizes its cost of production, we will spend this chapter examining firms’ costs. 2Measuring (ALL) Costs • Explicit costs are direct, out-of-pocket payments for inputs such as labor, capital, energy, and materials. • Implicit costs reflect a forgone opportunity. • The opportunity cost of a resource is the value of the best alternative use of that resource. • “There’s no such thing as a free lunch” refers to the opportunity cost of your time, an often overlooked resource. • Although many business people only consider explicit costs, economists also take into account implicit costs. 3Measuring (ALL) Costs • Capital is a durable good, which means it is a product that is usable for many years. • Difficult to measure the cost of a durable good • Initial purchase cost must be allocated over some time period • Value of capital may change over time; capital depreciation implies opportunity costs fall over time • Avoid cost measurement problems if capital is rented • Example: College’s cost of capital • Estimates of the cost of providing an education frequently ignore the opportunity cost of the campus real estate 4Example: Opportunity cost of steel Purchase steel for $1M. Since then, price has gone up so that it is worth $1.2M Two alternatives: 1) manufacture 2000 automobiles 2) resell the steel. What is the opportunity cost of manufacturing the cars? $1.2M, rather than $1M. • Costs depend on the perspective we take • Opportunity costs often are implicit 5Example: Investing $50M $50M to invest. 4 alternatives: 1) If invest now in CD-ROM factory, expected revenues are $100M. 2) If wait a year, expected revenues from CD-ROM investment are $75M. 3) If build new technology plant now, 50% chance that revenues are $0, 50% chance yields $150M. 4) If wait a year, will know whether revenues are $70M or $150M (each with probability ½). 6What is the opportunity cost of investing in CD-ROM plant now? Hence, 4) is the best alternative and the opportunity cost is $110M • Costs depend on the decision being made 3) yields .5($0) + .5($150M) = $75M 4) yields .5($70M) + .5($150M)=$110M 7Measuring (ALL) Costs • Opportunity costs are not always easily observed, but should always be taken into account in production decisions. • Sunk costs, past expenditures that cannot be recovered, are easily observed, but are never relevant in production decisions. • Example: Grocery store checkout line • Time spent waiting in a slow line should not influence your decision to switch to a different checkout line or stay put 8Sunk costs are costs that must be incurred no matter what decision is to be made. They are costs that have already been incurred and cannot be avoided. Non-sunk costs are costs that are incurred only if a particular decision is made and are thus avoided if the decision is not made. Sunk vs. Non-sunk Costs 9Example: Bowling ball factory It costs $5M to build and has no alternative uses $5M is not sunk cost for the decision of whether or not to build the factory $5M is sunk cost for the decision of whether to operate or shut down the factory 10This course: • Economic cost = opportunity cost, including explicit and implicit cost - The price per unit of labor (w): market wage rate - The price per unit of capital (r): market rental rate • Some cost is sunk in the short run (e.g., the capital investment) but all are non-sunk in the long run. So in the short-run, not all the inputs can be adjustable. 11Short-Run Costs • Recall that the short run is a period of time in which some inputs can be varied, while other inputs are fixed. • Short run cost measures all assume labor is variable and capital is fixed: • Fixed cost (F): a cost that doesn’t vary with the level of output (e.g. expenditures on land or production facilities). • Variable cost (VC): production expense that changes with the level of output produced (e.g. labor cost, materials cost). • Total cost (C): sum of variable and fixed costs (C = VC + F) 12Short-Run Cost Curves 13Short-Run Costs • To decide how much to produce, a firm uses measures of marginal and average costs: • Marginal cost (MC): the amount by which a firm’s cost changes if it produces one more unit of output. • Average fixed cost (AFC): FC divided by output produced • AFC = F / q • Average variable cost (AVC): VC divided by output produced • AVC = VC / q • Average cost (AC): C divided by output produced 14Short-Run Cost Curves 15Production Functions and the Shape of Cost Curves • The SR production function, determines the shape of a firm’s cost curves. • We can write q = g(L) because capital is fixed in the SR • Amount of L needed to produce q is L = g-1(q) • If the wage paid to labor is w and labor is the only variable input, then variable cost is VC = wL. • VC is a function of output: V(q) = wL = w g-1(q) • Total