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Intermediate Microeconomic Theory

Firm Behavior

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Profit Maximization

Given its technology, we now want to develop a model of firm behavior. Standard assumption: firms make decisions to

maximize profits, or maximize total revenue minus total costs.

where q = f(x1,…,xm)

Decision process can be broken up into two parts: What combination of inputs should firm use to produce

any given amount of output? (Production)

Given it makes the optimal production decision, how much should it produce/supply? (Supply)

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Production

We will consider first the Production decision. Key idea:

Consider any level of output for firm: q If firm is producing q in the profit

maximizing way, it must be producing q using the cost minimizing way (why must this be the case?

So, key to modeling production behavior is to analyze how input choices affect costs.

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Costs

When economists think about costs, they think much more broadly than do accountants.

Costs include not only direct costs that must be paid for, but indirect costs or “opportunity costs”

Opportunity cost - Lost revenue from failing to use an input factor for next best use.

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Costs

Suppose you currently have a job at a music store for $10/hr. and you currently have $1000 in your bank account earning interest of 1%/month.

Now say you are thinking of getting into the granola bar business. To produce 1000 granola bars, you would need 40 lbs of oats and 20 lbs of

honey (which you would have to buy up front). It will also take you 400hrs (1 month) to do the prep work and 200 hrs of oven time.

Suppose Oats cost $10/lb, and honey costs $5/lb. The going rate for oven rental time rent oven time is $6/hr., but you

already own an oven you can use.

What would be your total “economic” cost of producing 1000 bars?

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Iso-Cost Curves

Granola bars might take fixed inputs for any given level of output, but we will also often want to think about good for which there are trade-offs in the production process.

If we again consider the simple two-input case we can think of these trade-offs via Iso-cost curves. Iso-cost curves - all the combinations of inputs that

cost the same amount.

Ex: Suppose w1 = $10 w2 = $20 What is graph for the $100 Iso-cost curve? How about for the $200 Iso-cost curve?

What happens when input prices change?

So what is interpretation of slope of an iso-cost curve?

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Production Decision

Consider a firm with a technology given by a production function F(x1, x2) = x1

a x2b, and the

price of the inputs are w1 = 1 and w2 = 2 How would we graphically characterize the input

bundle that this firm want to use to produce 100 units of output?

How do you interpret this?

What about a different level of output, say q = 200?

What if prices were w1 = 2 and w2 = 2?

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Production Decision

So firm’s decision regarding which input bundle to use to produce a given level of output is similar (but not identical) to individual’s decision regarding the good bundle to use to produce utility.

Individual - Chooses bundle that is on highest Indifference Curve, but is still on budget constraint for $m.

(“Utility Maximization”)

Firm – To produce q units of output, choose input bundle that is on lowest Iso-cost curve, but still is on Isoquant curve for q.

(“Cost Minimization”)

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Conditional Factor Demands

In consumer theory, choice problem over good given different prices gives demand curve for goods.

In producer theory, choice problem over different inputs given prices gives conditional factor demands.

Denoted x1(w1, w2, q)

“conditional” because it gives demand for inputs conditional on producing some amount q.

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Conditional Factor Demand Curve

We can derive the Conditional Factor Demand Curve for a given input by choosing a given output level, then varying the price of one input while the holding prices of other inputs constant.

How do we derive this graphically?

How will this conditional demand curve change if we consider a higher level of output? How about higher prices for the other input?

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Conditional Factor Demands Analytically

How would we derive conditional factor demand function analytically? What to conditions hold at optimal input

bundle in example from above?

How do we use these to derive optimal input bundle for any given q?

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Conditional Factor Demand Curve Analytically So what will conditional factor demand curve look

like for input x1 given production function F(x1, x2) = x1

0.5x20.5, w1 = 2 and w2 = 8?

How about for input x2?

So if x1 and x2 are only inputs (i.e. no other opportunity costs), how much will it cost to produce 100 units of output? How about 200?

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Thinking about Conditional Factor Demand Curves Which would likely have a more elastic

factor demand curve---tax preparers or medical doctors?

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Is there (Middle Class) Life After Maytag?

Describe the “economics” of the changes in labor demand for Maytag.

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Is there (Middle Class) Life After Maytag?

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q=1000 q=1000 q=2000

$1 million isocost$700,000 isocost

$1.2 million isocost

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So how much money did “Maytag” save be re-optimizing production?

Besides the “economics,” what else does the article emphasize?