Topic 5 - Scanned Slides - Part 1 3.56.39 PM
MGEA02H Topic 5: Production, Productivity, and Costs
Understanding the Short Run Supply Curve
The focus is on comprehending diminishing marginal productivity and the shapes of cost curves in the short run.
Understanding these concepts is essential for grasping the supply curve and the decisions firms make regarding production levels.
Firm Objectives and Profit Maximization
Firms aim to maximize profits by:
Hiring labor and acquiring capital equipment and other inputs.
Utilizing available technology to combine these inputs to produce outputs.
Selling the produced output to generate profit.
Economic profit is calculated by subtracting total costs (including implicit opportunity costs) from total revenue:
( Economic \ Profit = Total \ Revenue - Total \ Cost )
( TR = P_x g L + P_k k = Total \ Revenue )
Example: Production Function in a Lawn Mowing Business
Assumption: One lawnmower as a fixed resource and returning to the production function:
1 Worker + 1 Lawnmower = 5 Lawns/day
2 Workers + 1 Lawnmower = 9 Lawns/day
3 Workers + 1 Lawnmower = 12 Lawns/day
4 Workers + 1 Lawnmower = 14 Lawns/day
5 Workers + 1 Lawnmower = 15 Lawns/day
Marginal Product of Labor (MPL):
5 lawns for the first worker
4 additional for the second worker
3 additional for the third worker
2 additional for the fourth worker
1 additional for the fifth worker
Average Product of Labor (APL)**
APL values for different workers:
5 lawns per worker for 1 worker
4.5 lawns per worker for 2 workers
4 lawns per worker for 3 workers
3.5 lawns per worker for 4 workers
3 lawns per worker for 5 workers
Definitions:
MPL: Marginal Product of Labor
APL: Average Product of Labor
Calculating Costs
Total cost equation: ( TC = P_x L + P_k K )
Given costs:
Rental cost of the lawnmower = $30/day
Wage per worker = $50/day
Total cost for different outputs:
For 5 lawns: $80
For 9 lawns: $130
For 12 lawns: $180
For 14 lawns: $230
For 15 lawns: $280
Average cost (AC) and marginal cost (MC) calculations:
( AC = \frac{TC}{Output} )
Changes in costs as output changes define MC.
Cost Curves
Cost curve insights:
As fixed inputs are involved in the short run, AC and MC curves maintain specific shapes.
Draw cost curves to visualize these relationships.
Inputs in Production Technology
Firms typically do not control production technology; they adopt existing technology, represented as:
( q = f(K, L) )
Where: K = physical capital (machinery, buildings), L = labor inputs (employed hours).
Production Function Examples
Cobb-Douglas Production Function:
( q = K^A L^B ) where parameters A & B > 0 and characteristics: A < 1 & B < 1.
A simpler version could be ( q = (KL)^{0.5} ) for specific cases.
Time Periods in Production
Definitions of time periods:
Short Run: Firms unable to change production capacity; K is fixed.
Long Run: Sufficient time for firms to alter plant capacity and new firms to enter/exit the market (K can vary).
Very Long Run: Time sufficient for technological changes to occur.
Short-run vs Long-run Production Functions
In the short run, production functions can be defined as:
( q = g(L) ) (K is fixed)
Diminishing marginal product expected:
( rac{dMPL}{dL} < 0 ) denotes diminishing returns.
Links Between Production and Costs
Total Economic Cost characteristics:
( TC = P_k K + P_L L )
Fixed cost (FC) and variable cost (VC) definitions in the short run:
FC = PKK
VC = PLL
Relationships between productivity and costs:
Average Variable Cost (AVC) at its minimum when Average Product of Labor (APL) is at its maximum.
Knowledge of APL allows inference on AVC.
Understanding Cost Curve Characteristics
Characteristic shapes of cost curves and their relationships:
Understanding their shapes means knowing productivity relationships, where:
If APL is inverted U-shape, AVC portrays a U-shaped curve.
The relationship between Marginal Product of Labor (MPL) and Marginal Cost (MC) reflects the same patterns.
Knowing these dynamics aids in competitive markets.