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Production Function

Various Production Functions. Linear Production FunctionQ = aK bLInputs are perfect substitutesMarginal Product of Labor = bLeontief Production FunctionQ = min(bk, cL)Also called the fixed proportions production functionInputs are perfect complements. Cobb-Douglas Production Function. Q = K

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Production Function

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    1. Production Function Production Function – a function that defines the maximum amount of output that can be produced with a given set of inputs. Q = f(K,L) Where K = Capital and L = Labor

    2. Various Production Functions Linear Production Function Q = aK + bL Inputs are perfect substitutes Marginal Product of Labor = b Leontief Production Function Q = min(bk, cL) Also called the fixed proportions production function Inputs are perfect complements

    3. Cobb-Douglas Production Function Q = KaLb Capital and Labor are both substitutes and complements for each other. Productivity of each input depends upon the amount of the other input employed Marginal Product of Labor = bKaLb-1

    4. On the Hiring of Workers Why do firms hire workers? Return to Cost-Benefit Analysis Cost = The wage the worker is paid. This is generally set in the market, not by the firm. Benefit = The productivity of the worker (marginal product) * the value of this productivity in the market place (price)

    5. VMP vs. MRP Value Marginal Product = Marginal Product of Labor * Price of Output Relevant when the firm has no control over market price. Marginal Revenue Product = Marginal Product of Labor * Marginal Revenue of Output Relevant when the firm has some control over market price.

    6. Profit Maximizing Hiring If W > MRP What action should the firm take? If W < MRP What action should the firm take? The firm will maximize profits with respect to the hiring of workers when W = MRP

    7. The Importance of Stage Two In what stage of production, then, do firms operate? Only in stage two. In stage one, increases in the labor force will increase the MRP. If it made sense to hire the previous workers, and the next worker offers a higher MRP, then it makes sense to hire the next. Hence firms will not stop hiring workers in Stage Two.

    8. The Long-Run How does a firm decide to expand production? Profit maximizing output > average cost minimizing output. Expanding productive facilities moves the firm from the short-run to the long-run. Long run - the shortest period of time required to alter the amounts of all inputs used in a production process. A period of time long enough for all inputs to be varied.

    9. Economies of Scale Economies of scale - reductions in the minimum average cost that come about through increasing plant size. specialization of labor. more efficient yet larger equipment. greater volume of output increase efficiency from learning. Constant returns to scale - increases in plant size do not affect minimum average cost.

    10. Diseconomies of Scale Diseconomies of scale - increases in plant size increase minimum average cost. supervision of workers more difficult (morale declines). lengthening of the managerial chain leads to disorganization. Long run average total cost is a summary of our best short-run cost possibilities.

    11. Economies of Scope Economies of Scope – when the total cost of producing two types of outputs together is less than the cost of producing each type of output separately

    12. Economic Efficiency Technical efficiency - as few inputs as possible are used to produce a given output. Economic efficiency - the method that produces a given level of output at the lowest possible cost. Economic efficiency is achieved when the amount of productivity received from each input per dollar spent is equal.

    13. Cost Minimization in the Long-Run The production of many goods does not follow a fixed recipe. How does the firm choose the inputs to use in production? MP1/P1 = MP2/P2 = ....... = MPn/Pn WHY IS THIS IMPORTANT? TO MAXIMIZE PROFITS YOU MUST COST MINIMIZE. HOWEVER, COST MINIMIZATION DOES NOT NECESSARILY MEAN PROFIT MAXIMIZATION.

    14. The Organization of the Firm The Multi-Plant Problem Cost-Volume-Profit Analysis (in book) Managerial Decisions Securing Inputs and Transaction Costs Managerial Compensation Worker-Management Relations

    15. Long-Run Average Cost Capacity – Output level at which short-run average costs are minimized. If a firm moves beyond ‘capacity’ the firm may want to consider building a larger plant. BE ABLE TO ILLUSTRATE THIS STORY IN THE SHORT-RUN Minimum Efficient Scale – Output level at which long-run average costs are minimized. BE ABLE TO ILLUSTRATE LONG-RUN AVERAGE COST AND IDENTIFY THE LEVEL OF OUTPUT CORRESPONDING TO MES.

    16. Firm Size and Plant Size Multi-plant Economies of Scale – Cost advantages from operating multiple facilities in the same line of business or industry. Multi-plant Diseconomies of Scale – Cost disadvantages from operating multiple facilities in the same line of business or industry.

    17. The Economics of Multi-Plant Operations Elements needed for problem Equation for Demand Curve Short-run Total Cost Function Steps in Solving the Problem Solve for profit maximizing output, price, and profit. Solve for average cost minimizing output. Solve for MC when firm produces at capacity. Set MR equal to MC at capacity to determine optimal multi-plant operation. Determine the optimal number of plants. Determine price and profit when firm employs the optimal number of plants.

    18. Methods of Acquiring Inputs: Spot Exchange Spot Exchange – an informal relationship between a buyer and seller in which neither party is obligated to adhere to specific terms for exchange. This is often used when inputs are standardized so effort in finding the ‘best’ input is not needed.

    19. Methods of Acquiring Inputs: Acquiring Inputs Via Contract Contract – a formal relationship between a buyer and seller that obligates the buyer and seller to exchange at terms specified in a legal document. Contracts can reduce uncertainty, but increase the transaction costs incurred by the firm.

    20. Methods of Acquiring Inputs: Internal Production Vertical Integration – a situation where a firm produces the inputs required to make its final product. Vertical integration (alternative definition)- various stages of production of a single product are conducted by a single firm. Motivation: Reduces Transaction Costs

    21. Transaction Costs Transaction costs - the expenses of trading with others above and beyond the price. i.e. the cost of writing and enforcing contracts. Transaction costs determine whether markets are internalized or allowed to remain external to the firm.

    22. More on Transaction Costs: The Work of Oliver Williamson Basic concepts that underlie transaction costs analysis. Markets and firms are alternative means for completing related sets of transactions. The relative cost of using markets or a firm’s own resources should determine the choice. The transaction cost of writing and executing contracts across a market is a function of the characteristics of the involved human actors the objective properties of the market In sum, both human and environmental factors impact the transaction costs across firms and markets.

    23. More from Williamson Purpose of this analysis is to identify the set of environmental and human factors that explain both internal firm and industrial organization. Key environmental factors: Uncertainty and number of firms Key human factors: Bounded rationality and opportunism

    24. Bounded Rationality and Opportunism Bounded rationality - the limited human capacity to anticipate and solve complex problems. Opportunistic behavior - Taking advantage of another when allowed by circumstances. High transaction costs: Specialized products: The creation of specialized products, where only a single buyer and/or seller exists, can lead to opportunistic behavior. This provides an incentive for vertical integration. Changing market conditions: Bounded rationality and uncertain market conditions make the writing and enforcement of contracts involving future conditions undesirable for both parties. Such high transaction costs increases the likelihood of vertical integration.

    25. Market vs. Internal Production Labor theory: Wages = Marginal Revenue Product Marginal Revenue Product = Marginal Revenue of Output (MR) * Marginal Product of Labor (MP) However, for this to be true for each worker a firm would need to measure MP. What if a firm cannot measure MP? Then a worker can reduce effort an still maintain the same wage. When monitoring costs are high, a firm has an incentive to sub-contract work. Why? For independent workers the wage (profit) is closer linked to productivity.

    26. More Benefits from Vertical Integration In addition to transaction costs, vertical integration is also motivated by two additional considerations. Vertical integration provides assurance of supplying inputs/outputs in a market that may be unstable. Threatens potential entrants by raising entry barriers (aluminum example)

    27. The Principal-Agent Problem A principal is the person who wants an action taken. In the work environment, this is the owner of the firm. The agent is the person who takes the action. In the work environment, this is the worker. If motivations differ between the principal and agent, and information is not perfect, a principal-agent problem exists. A specific example is the issue of moral hazard. Moral hazard occurs when the agent can take actions that the principal cannot directly observe that will reduce the welfare of the principal. For example, consider shirking. How can the firm limit shirking?

    28. Difficulty of Vertical Integration Shirking of Workers Shirking - the behavior of a worker who is putting forth less than the agreed to effort. Efficiency Wages – Paying the worker a wage above the market wage. Why is this necessary? Because workers can vary productivity, a firm may need to pay higher wages to ensure higher levels of output. Why would firms pay efficiency wages? In other words, why do higher wages elicit higher productivity. a. The Gift exchange hypothesis b. Worker turnover c. Worker quality

    29. Shirking Defense How do firms prevent the manager from shirking? Make the manager a residual claimant. Residual claimant - persons who share in the profits of the firm. How do firms prevent workers from shirking? Profit sharing – mechanism used to enhance workers’ efforts that involve tying compensation to the underlying profitability of the firm STOCK OPTIONS, etc.. Revenue sharing – mechanism used to enhance workers’ efforts that involve tying compensation to the underlying revenues of the firm SALES COMMISSIONS, TIPS, etc... NO INCENTIVE TO LOWER COSTS

    30. Teams and Productivity Teamwork is employed when a team of individuals can produce more than the sum of individuals working alone. Observing individual productivity is difficult, so shirking can occur: The Free Rider Problem Profit Sharing: If team members share in the profits of the firm, then they have an incentive to monitor other team members. If the incentive to monitor exceeds the free-rider effect, profit sharing can increase productivity.

    31. More Defense: Piece Rates Piece-Rate Compensation – Employee is paid according to productivity. Such a compensation plan will increase productivity. Will only work if productivity can be measured. Problems Teamwork will diminish. Quantity is easy to measure, quality is not. Thus quality can suffer with this compensation plan.

    32. Subjective Evaluations Why are subjective evaluations employed? To encourage innovation, dependability, cooperation, etc... Subjective evaluations can lead to rent-seeking by workers, or actions taken to re-distribute resources from others. Subjective evaluations can also be quite inaccurate. Inaccurate evaluations can distort incentives.

    33. The Role of Management What is the primary role of the manager? To prevent shirking, which limits the production of the firm. In essence, employees employ the manager to raise the return to the firm. Implications: If the manager is poor, employees will leave. If the returns of the firm do not accrue to the employees, the employees will leave. Remember, the labor market is like any other market. Exchange takes place by both parties because benefits exceed the costs.

    34. The Objectives of Management Managers seek to maximize utility (A.A. Berle and Gardner Means) Focus of these authors is on the separation of ownership and management, which arose due to the rise of the corporation. How would this impact market behavior? Studies have shown that managerial control is less profitable than owner control. Manager’s are more risk adverse, due to an inability to diversify. A related view.... Managers seek to satisfice (Richard Cyret, James March and Herbert Simon) In this class we assume that firms seek to maximize profits. This is a simplification. WHY DO WE NEED TO ANSWER THIS QUESTION? We need to know the motivation of the people we study.

    35. Why Profits? Why do firms make a profit? The story from classical economics Payment to the capitalist-entrepreneur (i.e. profit) is comprised of three elements (according to classical economics) payment for the use of capital payment to the entrepreneur for managerial expertise payment as compensation for risk What is profit in the long-run? How can profits persist?

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