Lecture11 - Lecture #11 Profit Maximization There are two...

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Lecture #11 Profit Maximization There are two ways to think about profit maximization. We can consider a firm that maximizes output with a given cost constraint (analogous to the consumer that aximizes total utility given their budget constraint) or we can think of a firm that maximizes total utility given their budget constraint) or we can think of a firm that minimizes their costs for a given level of output. 1. Output Maximization with a given Cost Constraint In a case where a firm faces a financial or cost constraint (it can only afford to spend a given amount of money on capital and labour) the profit maximization problem is: max π = TR – TC = P y ±-TC Y y We are assuming that the firm is a “price taker” in the output market (as in perfectly competitive markets. ..more soon) so that P Y is fixed. Since TC is also fixed by the firm’s cost constraint, we are only concerned with the one argument that can be varied . ..which is y. The firm’s profit maximization problem becomes one of maximizing y for a given cost . This is common in production situations where a department receives a production budget to follow and must maximize their output within the given budget.
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We can illustrate the solution to this problem with isoquants and isocost lines in much e same way as we solved the consumer’s utility maximization problem using the same way as we solved the consumer s utility maximization problem using indifference curves and budget lines. K K Isoquants Slope = MRTS = MP Isocost Slope = - w TC r y 3 p L MP K p r TC L L y 1 y 2 w K The necessary condition for profit maximization is that Given the fixed isocost line, the y y 2 A the slopes of the isocost and the isoquant are equal. This occurs only at point A where there is a point of highest possible isoquant (output level) is attained at point A. This is the 1 L tangency. This tangency condition is. .. point where the slope of the isocost line = the MRTS.
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MRTS = MP L = _w _ or MP L = MP K MP K r w r The sufficient condition is that isoquants be convex from the origin. If isoquants were concave (as in this raph) then y ould be the lowest not the highest K graph) then y 1 would be the lowest, not the highest, level of output attainable along the given isocost line. This is the same logic that we used in consumer equilibrium when we discussed concave indifference urves Now let’s consider the second way to think B curves. Now, let s consider the second way to think about profit maximization… L y 1 2. Cost Minimization with Output Given (Target Output) max π = TR – TC = P y ±–rK–wL If the firm has an output target (for example, a contract to produce one million basketballs) then the profit maximization problem for the firm becomes. .. Y which is simply to minimize total costs subject to an output requirement that is fixed (i.e. a fixed production run of one million basketballs).
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K Isoquant Slope = MRTS = MP K Isocost Lines Slope = - w = 1 million p L MP K r L y 1 million L Putting these graphs together we get the graphical representation of the cost minimization approach.
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This note was uploaded on 03/31/2011 for the course ECON 201 taught by Professor Vandewaal during the Fall '09 term at Waterloo.

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Lecture11 - Lecture #11 Profit Maximization There are two...

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