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ECON 230D1 (16)

Chapter 6-10.docx

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McGill University
Economics (Arts)
ECON 230D1
Jim Engle- Warnick

Chapter 6: Firms and Production 6.1 The Ownership and Management of Firms Private, Public and Nonprofit firms - Private sector: Owned by individuals or other non-governmental entities and whose owners try to earn a profit - Public sector: Firms and organizations that are owned by governments or government agencies - Non-for-profit sector: Organizations that are neither government-owned nor intended to earn profit o Pursue social or public interest objectives The Ownership for For-Profit Firms - Sole proprietorship: Firms owned by a single individual who is personally liable for the firm’s debts - General Partnership: Businesses jointly owned and controlled by two or more people who are personally liable for the firm’s debts - Corporations: Owned by shareholders in proportion to the number of shares of stock they hold o Limited liability: the personal assets of corporate owners cannot be taken to pa a corporation’s debts even if it goes into bankruptcy What Owners Want - To maximize profit -  = R – C - : Profit; R: Revenue; C: Cost - R = pq - p: Price; q: Quantity - Efficient production: if the firm cannot produce its current level with less inputs 6.2 Production - Capital service (K): Use of long-lived inputs such as land, buildings, and equipment - Labor service (L): Hours ofwork provided by managers, skilled workers, and less- skilled workers - Materials (M): Natural resources and raw goods and processed products Production Functions - The relationship between the quantities of inputs used and the maximum quantity of output that can be produced, given current knowledge of technology and organization - q = f (L,K) o Where q units are produced using L units of labor services and K units of capital o Function only shows the maximum amount of output that can be produced from given levels of labor and capital Time and the Variability of Inputs - Short run: The period of time so brief that at least one factor of production cannot be varied practically - Fixed input: A factors that a firm cannot vary practically in the short run - Variable input: Factor of production whose quantity the firm can change readily during the relevant time period - Long run: Long enough period of time that all inputs can be varied o No fixed inputs – all factors of production are variable inputs 6.3 Short-Run Production: One Variable and One Fixed Input - In the short run, we assume capital is a fixed input and that labor is a variable input o Increasing output by altering only labor - Production Function o q = f (L,K) o q: Output; L: Workers;K: Fixed number of unites of capital o It is the amount of output that a given amount of labor can produce holding the quantity of other inputs fixed - Marginal Product of Labor o MP = L o The exact relationship between output and labor - Average Product of Labor o AP = L o The ratio of output to the number of workers used to produce that output 6.4 Long-Run Production: Two Variable Inputs - Both capital and labor are variable - The firm can substitute one input for another while continuing to produce the same level of output, in much the same way a consumer can maintain a given level of utility - Cobb-Douglas Production Function a b o q = L K o L: Labor (workers) per day; K: Capital services per day Isoquants - Curve that shows the efficient combinations of labor and capital that can produce a single (iso) level of output (quantity) - If the production function is q = f(L,K) then the equation for an isoquant where output is held constant at q is o q = f(L,K) - Isoquants show a firm’s flexibility in producing a given level of output o Smooth curves because the firm can use fractional units of each input - Properties of Isoquants: o Same properties as indifference curves except that isoquants holds quantity constant whereas indifference curves hold utility constant o The farther an isoquant is from the origin, the greater the level of output o Isoquants do not cross o Isoquants slope downward o Isoquants must be thin - Shape of isoquants o The curvature of an isoquant shows how readily a firm can substitute one input for another o Extreme cases:  Inputs are perfect substitutes  If perfect substitutes, each isoquant is a straight line  Linear production: q = x+y  Inputs cannot be substituted for each other  Inputs must be in fixed proportions  Fixed proportion production function: q = min(g,b) o Where the min function means “the minimum number of g or b”  Isoquants would be in right angles  Imperfect substitution between inputs  Isoquants are convex  Along a curved isoquant, the ability to substitute one input for another varies  The marginal rate of technical substitution falls as labor increases n a convex isoquant Substituting Inputs - The slope of an isoquant shows the ability of a firm to replace one input with another while holding output constant - Slope of an isoquant is called the Marginal Rate of Technical Substitution o MRTS = o Tells us how many nits of capital the firm can replace with an extra unit of labor while holding output constant o Because isoquants slope downwards, MRTS is negative Diminishing Marginal Rates of Technical Substitution - The curvature of the isoquant away from the origin - As we move down and to the right along the isoquant, the slope becomes flatter – the slope gets closer to zero – because the ratio K/L grows closer to zero - The more labor the firm ha, the harder it is to replace the remaining capital with labor, so MRTS falls as the isoquant becomes flatter The Elasticity of Substitution - The percentage change in the capital-labor ratio divided by the percentage change in the MRTS - o Tells us how the input factor ratio changes as the slope of the isoquant changes o If the elasticity is large – a small change in the slope results in a big increase in the factor ratio – the isoquant is relatively flat o As the elasticity falls, the isoquant becomes more curved o As we move along the isoquant, both K/L and the absolute value of the MRTS change in the same direction, so the elasticity is positive 6.5 Returns to Scale - How much output changes if a firm increases all its inputs proportionately? Constant, Increasing, and Decreasing Returns to Scale - Increasing Returns to Scale o If output rises more than in proportion to an equal percentage increase in all inputs o Occurs when the firm is small with small amounts of output  Returns to specialization (workers and equipment) - Constant Return to Scale o When all inputs are increased by a certain percentage, output increases by that same percentage o Occurs when moderate amounts of output is produced – no returns to specialization and returns to scale are eventually exhausted - Decreasing Returns to Scale o If output rises less than in proportion to an equal percentage increase in all inputs o Occurs if the firm continues to grow and managing staff becomes more difficult so the firm suffers 6.6 Productivity and Technical Change Relative Productivity - Measure this by expressing the firm’s actual output, q, as a percentage of the output that the most productive firm in the industry could have produced, q*, from the same amount of inputs: 100q/q* Chapter 7: Costs - Explicit Cost: The wages and bills the sole proprietor must pay to conduct business - Implicit Cost: The opportunity cost s of resources owned by the firm – do not involve contractual payments 7.1 Measuring Costs Opportunity Costs - The value of the best alternative use of that resource 7.2 Short-Run Costs Short-Run Cost Measures - Fixed Cost, Variable Cost, and Total Cost o Fixed Cost: A cost that does not vary with the level of output o Variable Cost: The production expense that changes with the quantity of output produced o Total Cost: The sum of a firm’s variable and fixed costs  C = VC + F - Marginal Cost o The amount by which a firm’s cost changes if it produces one more unit of output o MC = - Average Cost o Average Fixed Cost (AFC): The fixed cost divided by the units of output produced  AFC = F/q  AFC rises because fixed cost is spread over more units o Average Variable Cost (AVC): The variable cost divided by the units of output produced  AVC = VC/q  AVC may either increase or decrease as output rises because the variable cost increases with output o Average Cost (AC): The total cost divided by the units of output produced  AC = C/q or AVC + AFC Production Functions and the Shape of Cost Curves - If a firm produces output using capital and labor and capital is fixed in the short run, the firm’s variable cost is its cost of labor o VC = Lw o L: Number of hours of Labor, w: Wage per hour - If the firm increases its labor enough, it reaches a point of diminishing marginal returns to labor, where each extra worker increases output by a smaller amount 7.3 Long-Run Costs Input Choice - Isoquant Line o The firm’s total cost is the sum of its labor and capital costs  C = wL + rK  wL: wage per hour x labor; rK: K hours of machine services at a rental rate of r per hour  o Isocost Line: The combination of labor and capital that cost the same amount  Where the isocost lines hit the capital and labor azes depend on the firm’s cost and the input prices  Isocosts that are farther from the origin have higher costs than those closer to the origin  The slope of each isocost line is the same  - Minimizing Costs o Three approaches to minimize cost:  Lowest Isocost rule – pick the bundle with the lowest isocost line touches the isoquant  Tangency rule – pick the nuble where the isoquant is tangent to the isocost  Last-Dollar Rule – pick the bundle of inputs where the last dollar spent on one input gives as much extra output as the last dollar spent on any other input o Firm chooses its inputs so that the MRTS equals the negative of the relative input prices   Shows the rate at which the firm can substitute capital for labor holding total cost constant o The firm minimizes the cost of production by selecting inputs such that MP Lw=MP /rK How Long-Run Cost Varies with Output - Expansion Path o The curve through the tangency points o The cost-minimizing combination of labor and capital for each output level - Long-Run Cost Function o Shows the relationship between the cost of production and output o C(q) = wL + rK Chapter 8: Competitive Firms and Markets 8.1 Perfect Competition Price Taking - Market is perfectly competitive if each firm in the market is a price taker that cannot significantly affect the market price for its output or the prices at which it buys inputs - A competitive firm would be a price taker if it faces a demand curve that is horizontal at the market price Why A Firm’s Demand Curve Is Horizontal - Firms are likely to be price takers in markets that have some or all of the following properties: o The market contains a large number of firms o Firms sell identical products o Buyers and sellers have full information about the prices charged by all firms o Transaction costs – the expenses of finding a trading partner and completing the trade beyond the price paid for the good or service are low o Firms can freely enter and exit the market Deviation of a Competitive Firm’s Demand Curve - Residual Demand Curve: the market demand that is not met by other sellers at any given price o D (p) o Shows the quantity demanded from the firm at price, p - Q = D(p) : The quantity the market demands - S(p) : The supply curve of the other firms - Thus, the residual demand function: o D (p) = D(p) - S(p) o When S(p) > D(p), the residual quantity demanded is 0 - The firm only sells to people who have not bought the same product from another seller - In equilibrium, D(p) = S(p) - Slope of the residual demand curve: o 8.2 Profit Maximization Profit -  = R – C o : Profit; R: Revenue, C: Cost Two Steps to Maximizing Profit - Output decision: If the firm produces what output level, q*, maximizes its profit or minimizes its loss? o Firm sets its output where its profit is maximized o Firm sets its output where its marginal profit is zero o Firm sets its output where its marginal revenue
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