Chapter 5 Econ- The production Process and Costs

Marginal Cost Function

MC(Q)= a +2bQ +3cQ^2

Marginal Cost (MC)

MC= dC/dQ

Changes for Isocosts:

-For given input prices, isocosts farther from the origin are associated with higher costs -Changes in input prices change the slopes of isocost lones

Marginal Rate of Technical Substitutions (MRTS):

-The rate at which a producer can substitute between two inputs and maintain the same level of output -absolute value of the slope of the isoquant MRTSkl=MPl/MPk

Isocosts:

-combination of inputs that yield the same cost. wL + rK = C -> wage rate(labor) +rent(capital)=cost

Diseconomies of Scale (^Q ----> ^LRAC)

1. Crowds out 2. as number of tasks increase, harder to manage effectively 3. the advantage on buying in bulk diappears

The manager's role in the production process:

1. produce output on the production function (aligning incentives to induce maximum worker effot) 2. Use the right mix of inputs to maximize profits

Reasons for Econ of Scale (^Q ----> lower LRAC)

1. specialization 2. flexibility (more choices of inout bundles) 3. advantages in buying in bulk

Principle of Irrelevance of Sunk Costs

A decision maker should ignore sink costs to maximize profits or minimize loses

Average product maximized when

APl= MPl

Average Total Cost (ATC)

ATC= AFC +AVC ^ ^ (FC/Q) + (VC/Q)

Economies of Scale

Declining Portion of the long-run average cost curve as output increases

The Cubic Cost Function

C(Q)= f + aQ + bQ^2v + cQ^3

Algebraic Form for a Multi product Cost Function

C(Q1,Q2)= f + aQ1Q2 + (Q1)^2 + (Q2)^2 -MC1= aQ2 + 2Q1 -When a < 0, an increase in Q2 reduces the marginal cost of producing 1. -If a<0, this cost function exhibits cost complementarity -if a>0, there are no cost complementarities -exhibits economies of scope whenever f-aQ1Q2 >0

Fixed Costs

Cost that does not change with output

Sunk Cost

Cost that is forever lost after it has been paid

Cost Complementarity

Exist when the marginal cost of producing one type of output decreases when the output of another good is increased. (change in MC1 (Q1,Q2)/ change in Q2) <0 ex. donuts vs donut holes

Economies of Scope:

exists when the total cost of producing Q1 and Q2 together is less than the total cost of producing each of the type of output separately. C(Q1,0) + C(0,Q2) > C(Q1,Q2)

Long Run

Period of time over which all factors of production (inputs) are variable and can be adjusted by a manager (ALL FACTORS are variable)

Linear:

Q = F(K,L) = ak+ bL; where a and b are constants

Cobb-Douglas:

Q= F(K,L) =K^aL^b, where a and b are constants *most used function

Leontief:

Q=F(K,L) = min{aK,bL}, where a and b are constants. ex. K=1, L=1 Q=F(3k,4k) Q= F(3(1), 4(1)) -----> min{3,4} L-shaped Graph

Diseconomies of scale

Rising portion of the long-run average cost curve as output increases

Marginal Product (MP):

The change in total product (output) attributable to the last unit of an input Marginal Product of Labor: MPl= dQ/dl Marginal Product of Capital: MPk= dQ/dk

Optimal Input Substitution

To minimize the cost of producing a given level of output, the firm should use less of an input and more of other inputs when that input's price rises (when prices change, substitutes ^)

Long-run average cost curve

a curve that defines the minimum average cost of producing alternative levels of output allowing for optimal selection of both fixed and variable factors of production

Multiple-Output Cost Function: Suppose a firm produces two goods and has cost function given by: C= 100 -0.5Q1Q2 + (Q1)^2 +(Q2)^2; if the firm plans to produce 4 units of Q1 and 6 units of Q2 -does the cost exhibit cost complementaries? -does this cost function exhibit economies of scope?

a= -.5<0 ---> yes, cost complementarities exist 100-(-.5)(4)(6)>0 Yes, economies of scope exist

Isoquants:

capture the tradeoff between combinations of inputs that yield the same output in the long run, when all inputs are variable

The Production Function:

mathematical functions that defines the maximum amount of output that can be produced with a given set of inputs. Q= F(K,L) where: Q= the level of output K= quantity of capital input L= the quantity of labor input

Total Product (TP):

maximum level of output that can be produced with a given amount of inputs ex. Machine produces what it is told to. WILL produce as many as said

Average Product (AP):

measure of productivity. A measure of the output produced per unit of inout Average Product of Labor: APl= Q/l Average Product of Capital: APk= Q/k

Short Run

period of time where some factors of production (inputs) are fixed, and constrain a manager's decision (ATLEAST ONE variable is fixed)

Constant returns to scale

portion of the long-run average cost curve that remains constant as output increases

cost-minimizing input rule (optimum point of minimizing costs)

produce at a given level of output where the marginal product per dollar spent is equal for all input: MPL/W = MPK/r or MPL/MPK = W/r ^L --> lowers MPL; ^MPK ----> lowers k

Cost Minimization

producing at the lowest possible cost

Point of inflection

when marginal product is at it's peak