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Short Run Production Function
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the maximum quantity of a good or service that can be produced by a set of inputs, assuming at least one input used remains unchanged (fixed).
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Long Run Production Function
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the maximum quantity of a good or service that can be produced by a set of inputs, assuming the firm is free to vary the amount of all the inputs being used. Total output increases when both outputs (ex: X and Y from 6.1 and table 6.5) increase by 1 unit. The result is called Returns to Scale.
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Increasing Returns to Scale
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increase in a firm's inputs by some proportion results in an increase in output by a greater proportion the firm experiences increasing returns to scale.
Thus, if Eq > 1 we have increasing returns to scale (IRTS)
Thus, if Eq > 1 we have increasing returns to scale (IRTS)
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Constant Returns to Scale
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If output increases by the same proportion as the input increase, the firm experience constant returns to scale.
If Eq = 1 we have constant returns to scale (CRTS)
If Eq = 1 we have constant returns to scale (CRTS)
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Decreasing Returns to Scale
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A less than proportional increase in output is called decreasing returns to scale.
If Eq < 1 we have decreasing returns to scale. (DRTS)
If Eq < 1 we have decreasing returns to scale. (DRTS)
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Returns to Scale
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One way to measure returns to scale is to use a coefficient of output elasticity, Eq:
Eq = % change in Q/ % change in all inputs
Eq = % change in Q/ % change in all inputs
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Cobb-Douglas Production
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Q=aL^bK^c
- Power function in which total quantity produced is the result of the product of inputs raised to some power.
- The two inputs are L (manual workers) and K (fixed capital)
- Both inputs must exist for Q to be a positive number
- Function can exhibit increasing, decreasing or constant returns:
If, b + c > 1, returns to scale are increasing
If, b + c < 1, returns to scale are decreasing
If, b + c = 1, constant returns exist
- Elasticities of the factors are equal to their exponents (example b and c). Thus, the elasticities of labor and capital are constants
- Power function in which total quantity produced is the result of the product of inputs raised to some power.
- The two inputs are L (manual workers) and K (fixed capital)
- Both inputs must exist for Q to be a positive number
- Function can exhibit increasing, decreasing or constant returns:
If, b + c > 1, returns to scale are increasing
If, b + c < 1, returns to scale are decreasing
If, b + c = 1, constant returns exist
- Elasticities of the factors are equal to their exponents (example b and c). Thus, the elasticities of labor and capital are constants
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Power Function
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Q = aL^b
- A major advantage of the power function is that it can be transformed into a linear function when it is expressed in logarithmic terms, making it amenable to linear
- regression analysis: log Q = loga + blogL
- The direction of the marginal product depends on the size of the exponent b.
If b>1, marginal product is increasing
If b=1, it is constant
If b<1, it is decreasing
- In simple 2 variable model, the power function permits the estimation of marginal product and returns to scale. (2 variable model example: labor & capital); (marginal product example: labor changes and capital remains the same) and (returns to scale example: when both variables change)
- A major advantage of the power function is that it can be transformed into a linear function when it is expressed in logarithmic terms, making it amenable to linear
- regression analysis: log Q = loga + blogL
- The direction of the marginal product depends on the size of the exponent b.
If b>1, marginal product is increasing
If b=1, it is constant
If b<1, it is decreasing
- In simple 2 variable model, the power function permits the estimation of marginal product and returns to scale. (2 variable model example: labor & capital); (marginal product example: labor changes and capital remains the same) and (returns to scale example: when both variables change)
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Various Forms of Production Functions
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• Short Run
• Cubic
• Quadratic
• Straight-line (linear)
• Power
• Cubic
• Quadratic
• Straight-line (linear)
• Power
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Quadratic Cost Function
answer
TC = a + bQ + cQ^2
MC = b +2cQ
AC = a/Q +b +cQ
MC = b +2cQ
AC = a/Q +b +cQ
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Linear Cost Function
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TC = a + bQ
MC = b
AC = a/Q + b
MC = b
AC = a/Q + b
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Rules of operations for Quadratic formula
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1. Paratheses
2. Multiplication
3. Division
4. Addition
5. Subtraction
6. Inside square root box
- Do all operations under square root box first IN ORDER then take square root
2. Multiplication
3. Division
4. Addition
5. Subtraction
6. Inside square root box
- Do all operations under square root box first IN ORDER then take square root
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Rules for Elasticities
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Elastic - demand for luxury goods (furs, gems, expensive automobiles)
Inelastic - demand for goods considered to be necessities (milk, shoes, electricity)
Elastic > 1
Inelastic < 1
Unit Elastic = 1 (in absolute terms)
Inelastic - demand for goods considered to be necessities (milk, shoes, electricity)
Elastic > 1
Inelastic < 1
Unit Elastic = 1 (in absolute terms)
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T-Test Rule
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basic test of statistical significance of each regression coefficient. Interpreting the value of t, use the t-table .05 level of significance. T-test only applies to each individual coefficient.
Rule of 2: this means that IF the absolute value of t is greater than 2, then it is significant at the .05 level.
Rule of 2: this means that IF the absolute value of t is greater than 2, then it is significant at the .05 level.
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R^2(Coefficient of determination or R2) Rule
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shows the percentage of the variation in a dependent variable accounted for by the variation in all the explanatory variables in the regression equation. Closer R^2 is to 1.0 the greater the explanatory power of the regression analysis. (Example: pizza regression, R^2 = .885, means 88% of variation in demand for pizza can be accounted for by the explanatory variables such as: (price, cost of tuition, soft drink)
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F-test Rule
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Often used in conjunction with with R^2. This test measures the statistical significance of the entire regression equation. Either valued on .05 or .01 level, higher is significant and less is insignificant
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Factors for Outsourcing
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1. reduce costs - wage differentiation vs. productivity differentiation
2. specialization
3. tax incentives
4. location & transportation costs
5. social factors
6. ease of doing business in another country
2. specialization
3. tax incentives
4. location & transportation costs
5. social factors
6. ease of doing business in another country
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Are opportunity costs relevant or irrelavant?
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Relavant
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Are Replacement costs relevant or irrelavant?
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Relavant
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Are Sunk costs Relevant or Irrevalant?
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Irrelavant (in the past)
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Long Run Total Costs
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- In long Run Total Costs, there are no fixed costs
TC=TVC
In increasing returns to scale; costs will increase slowly
<------- on graph
In decreasing retursn to scale; costs increase quickly
---------> on graph
in between is constant returns to scale
TC=TVC
In increasing returns to scale; costs will increase slowly
<------- on graph
In decreasing retursn to scale; costs increase quickly
---------> on graph
in between is constant returns to scale
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Long Run Average Total Cost
answer
Economies of Scale: AS scale of operations increases Average Costs fall
<--------on graph
Diesconomies of Scale: As scale increases average cost will increase
---------> on graph
<--------on graph
Diesconomies of Scale: As scale increases average cost will increase
---------> on graph
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What happens in Economies of Scale?
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In production - technology taken advantage at larger scale; Specialization
In Costs - Bulk of discounts; consolidate admin functions;
Efficient supply chain; lower cost of capital borrowing; lower costs of R&D and advertising/marketing
In Costs - Bulk of discounts; consolidate admin functions;
Efficient supply chain; lower cost of capital borrowing; lower costs of R&D and advertising/marketing
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What happens in Diseconomies of Scale?
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Scarcity of resources due to costs; bueracracy (HR); management & monitoring; storage/transportation (inventory); compliance
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Relationship between Long Run & Short Run
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In the short run averaget total costs are fixed; after in long run envelops all short run curves
(Example on a graph: (Q1)Year 1-5 firm owns 1 shop; (Q2) Year 5-10 firm owns several shops in Tampa Bay; (Q3) Year 10-15 in the state; and (Q4) then in southern region)
Between Q3 and Q4 it is the middle of short run average total cost curves and long run average total cost curves is EFFICIENCY
(Example on a graph: (Q1)Year 1-5 firm owns 1 shop; (Q2) Year 5-10 firm owns several shops in Tampa Bay; (Q3) Year 10-15 in the state; and (Q4) then in southern region)
Between Q3 and Q4 it is the middle of short run average total cost curves and long run average total cost curves is EFFICIENCY
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In Data/Regresson Analysis
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Y is dependent variable
X is independent variable
Independent variable are the things to choose for regression analysis (ex: labor and capital)
X is independent variable
Independent variable are the things to choose for regression analysis (ex: labor and capital)
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Reporting on Natural Logs:
answer
Y = 3X + 6
3 would be the coefficient
6 is the intercept
Logs look like:
LnQ = intercept + coefficient (LnL) + coefficient (LnK)
Q = Quantity
L = Labor
K = Capital
3 would be the coefficient
6 is the intercept
Logs look like:
LnQ = intercept + coefficient (LnL) + coefficient (LnK)
Q = Quantity
L = Labor
K = Capital
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R^2 meaning
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Example: data shows R^2 as 0.945
Therefore 94.5% of the variation in quantity is explained by the equation
As we change labor & capital 94.5% of quantity is due that change.
Best fit is finding the highest R^2
Therefore 94.5% of the variation in quantity is explained by the equation
As we change labor & capital 94.5% of quantity is due that change.
Best fit is finding the highest R^2
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Statistical Significance: Rule of 2
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If t-stat is more than 2 then it is significant or less than -2 is significant
Significant means if we change labor that it changes qauntity; Meaning, quantity & labor are related strongly
Significant means if we change labor that it changes qauntity; Meaning, quantity & labor are related strongly
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Marginal Product Labor (MPL)
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MPL is only looked at in short run.
Coefficient of L, it is either less than or greather than 1; MPL increasing if greater than 1; MPL decreasing if lesser than 1
APL = MPL is when it is at its maximum
Coefficient of L, it is either less than or greather than 1; MPL increasing if greater than 1; MPL decreasing if lesser than 1
APL = MPL is when it is at its maximum
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Outsourcing benefits
answer
cost savings
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Outsourcing costs
answer
1. risk in quality
2. research costs
3. risk of competition
4. transportation costs
5. infrastructure
6. intangible costs
7. coordination costs
8. transaction costs (contracts, negotiations)
2. research costs
3. risk of competition
4. transportation costs
5. infrastructure
6. intangible costs
7. coordination costs
8. transaction costs (contracts, negotiations)
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How to lower costs other than outsourcing?
answer
1. Techonology improvement
2. training for better work efficiency
3. decrease assets
4. layoffs
5. lean production (managing inventory & forecast demand very well)
6. mergers
7. innovations
2. training for better work efficiency
3. decrease assets
4. layoffs
5. lean production (managing inventory & forecast demand very well)
6. mergers
7. innovations
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Economies of Scope
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increaseing scope of production (diversifying)
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Short run analysis:
answer
time series data for a limited time
(Don't need to worry to collect data for fixed factor)
(Don't need to worry to collect data for fixed factor)
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Marginal Cost Curve:
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The supply curve is reflective (mirrors) of marginal cost curve.
MC curve upward sloping which is consistent with cubic cost function.
MC curve upward sloping which is consistent with cubic cost function.
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How to estimate long run functions:
answer
1. Better to use cross sectional data (across locations so we can see different scales
2. May be regional differences or factor prices across the board.
3. Relative differences between/among factor prices
4. If looking at different firms need to look at the accounting methods being consistent across firms
5. When looking at results look at averages
2. May be regional differences or factor prices across the board.
3. Relative differences between/among factor prices
4. If looking at different firms need to look at the accounting methods being consistent across firms
5. When looking at results look at averages
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Natural Monopoly
answer
Firms that get better as they get bigger; always experience economies of scale
(IE: electricity is natural monopoly)
(IE: electricity is natural monopoly)
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Average Total Cost (ATC)
answer
1. When its in equilibrium then economic profit is zero
2. No further entry or exit by any firms when in equilibrim
3. Long run equilibrium - the perfectly competitive firm operates at a minimum point on its ATC curve = EFFICIENT
2. No further entry or exit by any firms when in equilibrim
3. Long run equilibrium - the perfectly competitive firm operates at a minimum point on its ATC curve = EFFICIENT
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Long Run
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As long as TR > TC firm should stay open
IF, TRC < TC then firm should exit industry
d=p=mr
demand=price=marginal revenue
IF, TRC < TC then firm should exit industry
d=p=mr
demand=price=marginal revenue
question
4 Types of market structures
answer
1. Perfect Competition
2. Monopoly
3. Monopoly Competition
4. Oligopoly
Market Structures are defined by degree of market power
2. Monopoly
3. Monopoly Competition
4. Oligopoly
Market Structures are defined by degree of market power
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Market Power
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Market Power is how much control over the price that is charged. Market power depends on how much competition firm faces (how many firms are in the idustry?)
A firm is one unit of production. A collection of firms is industry market.
A firm is one unit of production. A collection of firms is industry market.
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Characteristics that define market structures:
answer
1. ease of entry or exit
2. short run vs. long run profit
3. ability to differentiate product
4. degree of information about the market & their competitors/ market
2. short run vs. long run profit
3. ability to differentiate product
4. degree of information about the market & their competitors/ market
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Pefect Competition
answer
A lot of firms
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Monopoly
answer
1 firm
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Oligopy
answer
few firms
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Perfect Competition Characteristics
answer
Lots of firms; no product differentiation (homogenous); easy entry & exit
- This applies to all: Profit maximizers (economic profit) & (costs include opportunity costs)
- Profit = TR-TC
- Perfect Information - All buyers and sellers know same information & particularly about pricing
- Perfectly competitive firms is a PRICE TAKER; meaning take price GIVEN from market
- (Example of Price Takers - hot dog stand industry; gas station coffee)
- In perfect competition ONLY price = Marginal Revenue (P=MR)
- This applies to all: Profit maximizers (economic profit) & (costs include opportunity costs)
- Profit = TR-TC
- Perfect Information - All buyers and sellers know same information & particularly about pricing
- Perfectly competitive firms is a PRICE TAKER; meaning take price GIVEN from market
- (Example of Price Takers - hot dog stand industry; gas station coffee)
- In perfect competition ONLY price = Marginal Revenue (P=MR)
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Calculation for Price =Marginal Revenue (P=MR)
answer
MR = dTR/dQ
=PdQ/dQ +dP/dQ Q
=P*1
=PdQ/dQ +dP/dQ Q
=P*1
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Maximization of Profit
answer
- biggest difference between TR+TC
(Peak of a profit curve)
Change^Profit/^Quantity = 0 (marginal profit)
^(TRC-TC) / ^Q = 0
MR - MC = 0
Set Marginal Revenue to Marginal Costs MR=MC
MR = MC rule holds for all industry forms
Profit max is loss minimization ATC is above price (P) line
(Peak of a profit curve)
Change^Profit/^Quantity = 0 (marginal profit)
^(TRC-TC) / ^Q = 0
MR - MC = 0
Set Marginal Revenue to Marginal Costs MR=MC
MR = MC rule holds for all industry forms
Profit max is loss minimization ATC is above price (P) line
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When does firm cut losses when losing revenue?
answer
In the short run, stay open (incur loss) if
(TR-TC) < 0
Total Cost (TC) is TFC + TVC
If shuts down, no revenues but will still have fixed costs (TFC)
AS long as TR > TVC stay open
Can variable costs be covered?
(TR-TC) < 0
Total Cost (TC) is TFC + TVC
If shuts down, no revenues but will still have fixed costs (TFC)
AS long as TR > TVC stay open
Can variable costs be covered?
question
Example: What are the elasticities of production of labor and capital in this calculation:
Q = 2.64 L^0.622 K^0.359
Q = 2.64 L^0.622 K^0.359
answer
Labor's coefficient 0.622 is less than 1 so it is inelastic
Capital's coefficient is 0.359 is less than 1 so it is inelastic
Capital's coefficient is 0.359 is less than 1 so it is inelastic
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In the short run, is the marginal product of labor increasing or decreasing?
Q = 2.64 L^0.622 K^0.359
Q = 2.64 L^0.622 K^0.359
answer
MPL is decreasing because 0.622 is less than 1
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