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Chapter 13 - 14 Marginal Costs, Revenue, Profits

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Keith Diaz Chapter 13 -14: Marginal Product, Costs, Revenue, and Profit Production Function  The relationship between the quantity of inputs (workers) and quantity of outputs  Total product (TP) is the total amount of output that is produced during a given period of time  Average product (AP): (of a variable factor) is the TP divided by the number of units the variable factor used to produce it. Since labor is usually the most important variable factor in the short run, we usually talk of the average product of labour: AP = TP / L Marginal Product  increase in output (TP) arising from an additional unit of that input, holding all other inputs constant  helps firms decide whether they can produce more from more inputs  MP = ∆TP / ∆ L  slope of the production function (TP); diminishes as L rises because TP gets flatter  Law of diminishing returns: if increasing amounts of a variable factor are applied to a given quantity of the fixed factor, eventually the marginal product of the variable factor declines. - Ex: a worker who does everything required to manufacture a product. As more workers are added, each can specialize on one task, and marginal product rises. BUT if there is a fixed amount of physical capital, eventually the marginal product begins to decline (could be negative) Relation between AP and MP 1) MP > AP, MP rising  then law of diminishing returns kicks in: MP falls while AP keeps rising 2) When MP = AP, it is the maximum of AP. (if the marginal thing = average, average won’t change) 3) When MP < AP, AP falls as the MP of each additional worker is less than average, pulling down AP Relation between TP and MP 1) When TP is rising at an increasing rate (concave up), MP is positive and rising 2) When TP is rising at a decreasing rate (concave down), MP is positive and falling 3) When TP is at its maximum, MP is at 0 in the short run 4) When TP is falling, MP is negative (below Q Labour axis) Cost function  Relationship between Q and cost of production  The curve gets steeper as Q increases because of diminishing marginal product  Total cost = fixed cost + variable costs  Average total cost = AFC + AVC = (FC + VC) / Q - ATC curve U-shaped because initially, falling AFC pulls ATC down, then rising AVC pulls ATC up.  Fixed cost: do not vary with Q produced  average fixed cost: AFC = FC / Q - This is a sunk cost: a cost that has already been committed and cannot be recovered. You must pay them regardless of your choice. A firm must pay its fixed costs whether it shuts down or not. - If you bought a ticket for $10, and value a movie for $15, buy another one even if you lose it  Variable costs: vary with Q average variable cost: AVC = VC/Q  rises as Q rises, eventually - Example: fixed cost would be the cost of land, variable cost would be the wages or material cost - Find the variable costs at different quantities  Economies of scale: ATC falls as Q increases (more common when Q is low) - Occurs when increasing production allows greater specialization and more efficiency  Constant returns to scale: ATC stays the same as Q increases  Diseconomies of scale: ATC rises as Q increases (more common when Q is high) - Due to coordination problems in large organizations Keith Diaz Marginal Cost  The increase in TC from producing one more unit supply curve = Q willing to supply at any P - P is value to buyers of the marginal unit decide whether it’s worth the cost to produce more  In the short run, competitive firms (equilibrium) produce where P(market price) = MC  MC = ∆ TC / ∆ Q  usually rises as Q rises Relation between MC and ATC  The MC curve crosses the ATC curve at the ATC curve’s minimum - At low levels of output, MC < ATC, so ATC is falling. - But when the 2 curves cross, MC = ATC at minimum ATC = efficient scale (break even; 0 profit) - MC > ATC, so ATC must start to rise at this level of output.  If where MC = ATC is less than the market price, (firm is producing at lower costs) the firm should produce more, at the market price  produce at P where D = MC Costs in the Short run and Long run  Short run: some inputs are fixed  costs of these are the FC (fixed costs)  Long run: all inputs are variable; curve is much flatter due to more flexibility factory size variable  In LR, ATC at any Q is cost per unit using the cost efficient mix of inputs for that Q - minimums of each SRATC curve form the points of the LRATC firm’s LR cost curve uses the most efficiency factory size with the lowest ATC - efficient scale: level of production with lowest ATC Characteristics of Perfect Competition 1. Many buyers and many sellers 2. The goods offered for sale are largely the same 3. Firms can freely enter or exit the market no barriers (government does not restrict # firms)  1 and 2 means that each buyer and seller is a price taker: takes the price as given  Competitive firm has an upward sloping total revenue curve and horizontal demand  In the LR, supply curve is horizontal and in SR demand is horizontal? Revenue of a Competitive Firm  Total revenue = P x Q - Because everyone’s a price taker, Q doesn’t affect P, and hence TR is proportional to Q.  Average revenue (AR) = TR / Q = P  Marginal revenue (MR): ∆ TR / ∆ Q; the change in TR from selling one more unit - For a competitive firm (can keep increasing its output without affecting the market price), each one-unit increase in Q causes the revenue to rise by P. Hence, MR = P = AR (NOT TR)  Total revenue is maximized when MR = 0 Keith Diaz P
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