Marginal Analysis:- Optimization techniques provide a decision rule that will allow us to choose the best decision from a set of alternatives.- Optimal managerial decisions involve comparing benefits to a decision against the associated costs of that decision.- Marginal Analysis will allow us to use optimization techniques to make sound business decisions.Graph of Benefits (R):

Benefits (revenues) are assumed to come from demand analysis:- The equation for such a line isP = a – (b*Q)- Revenuesthen are given by P*Q, thus TR = (a –bQ)*Q = aQ – bQ^2- We want **MC = MR**- MR = Δ(TR)/ΔQ- MC = (TC)/ QΔ Δ- Managers want tomaximize profits (Net Revenue)by setting marginal profits (Marginal Net Revenue) (M ) = 0π- Remember that MB and MC will vary at different quantities. (See graph):

Marginal Profit Approach:- Get Mπ (take derivative of π) then set M = 0πMR/MC Approach:- Get MR and MC then set MR=MCRevenue Maximization with x and y:

When given an inverse demand function P = a – (b*q) and a TC equation:Steps to Maximiizing Profit:

- Step 1: solve for TR by multipling P by Q- Step 2: Solve for π by computing TR –TC = π- Step 3: Compute marginal profits (M )π by taking derivative of .π- Step 4: Set M = 0π and solve for profit maximizing Q- Step 5: Plug Q back into πequation to find optimized profits.

Supply and Demand:- Demand curve: address intentions to purchase (consumer or demand side)-the amount of good or service that consumers are willing and able to purchase from market.- Supply curve: address intentions to supply (producer or supply side)-the amount of a good or service that producers are willing and able to offer/supply to market.- Equilibrium: the price and quantity that correspond to where the amount producers are willing to supply equal the amount that consumers are willing to purchase.- In a free market, the equilibrium price is determined from simultaneous interaction of supply and demand curves.- Price Ceiling: The government can impose a price ceiling (a maximum price allowed to be charged) if they think that the equilibrium price is too high. This causes a shortage (The quantity supplied is less than the quantity demanded).- Price Floor: A minimum price charged that is imposed when the government believes that the equilibrium price is too low. This causes a surplus (the quantity supplied is greater than the quantity demanded).Demand Curve:

Determinants ofquantity demandedPrice (P), Price of substitute goods (Ps), Price of complementary goods (Pc), Income (Y), Advertising (A), Advertising by

Competitors (Ac), Size of population (N), Expected future prices (Pe), Adjustment time period (Ta), Taxes or subsides (T or S).Change in quantity demanded: A movement along a demand curve that occurs when the price of the good changes, all else constant.Change in Demand: A shift in the demand curve, either leftward or rightward, that occurs only when one of the determinants of demand-not including price-changes.Supply Curve: Determinants of Supply Function: Price (P), Input Prices (PI), Price of unused substitute goods (PUI), Technological improvements (T), Entry and exit of other sellers (EE), Accidental supply interruptions (F), Cost of regulatory compliance (RC), Expected future changes in price (PE), Adjustment time period (TA), Taxes or Subsidies (T or S).Budget Line: shows the various combinations of X and Y that the consumer can purchase based upon his/her income.Consumer Surplus: The value that the consumer gets but does not have to pay for (what the would have paid versus what they actually paid)- Calculate: Take the area of the triangle above the market price and what the consumer was willing to pay (1/2 base*height).Producer Surplus: Value that producers receive versus the value that induces them to produce.- Calculate: the area of the triangle under the market price (1/2 base*height).Elasticity: Equal to the percent change in quantity demanded divided by the percent change in price. Measures the responsiveness of a good’s sales to changes in its price.E = |%ΔQ / %ΔP|**(remember absolute value)**But remember that + or – indicates the direction that the elasticity is talking about.E > 1 = ElasticE = 0 Perfectly InelasticE < 1 = InelasticE = 1 Unit ElasticE = ∞ Perfectly ElasticGiffen or Veblen Goods: Goods that don’t conform to laws of demand, and have positive E. (Luxury goods).

- Ex: E = -2 means a 10% increase in price means a 20% decrease in quantity demanded.- Price and quantity are negatively related by the Law of Demand so E is always negative. By convention, when we compute the elasticity of demand, we take the absolute value.- Elasticity is NOT the same as slope. Slope measures change in quantity as price changes. Elasticity measures the percentage change in Q relative to the percentage change in P.- Point Elasticity: If we know the form of the demand function (linear), then we writeEp= (ΔQ/ΔP)*(P/Q)

Determinants of Ep:- # of substitutes (more subs = more elastic)- share of total budget allocated to spend on a certain product (spending a smaller % of income on a good = inelastic demand).- durability of product- time frame (longer time = more elastic)Income Elasticity: Measures the responsiveness of quantity demanded to changes in income, M, holding the price of a good and all other determinants of demand for the good constant.E = %ΔQ / %ΔMPositive = Normal goodNegative = Inferior goodCross Price Elasticity: measures the responsiveness of quantity demanded of good X to changes in the price of a related good Y, holding the price of good X and all other determinants of demand for good X constant.Exy = %ΔQx / %ΔPy

Exy> 0 -> X and Y are substitutesExy< 0 -> X and Y are complementsUsing demand functions with elasticity:

Changes in Revenues when you have more than one good: ΔR = [Rx (1+EQx,Px) + RYEQY,Px] x %ΔPx

MR = P [ 1 + 1 / Ep ]Revenues are maximized where Ep = -1 and MR = 0For linear demand E & price vary directlyIf |E| > 1 then MR > 0If |E| < 1 then MR > 0P = a – bQTR = PQ = aQ – bQ2

MR = a - 2bQMarkup Pricing:MC = [Ep/(1+Ep)] – 1 = (P-MC)/MC where MC=MRWhen there is NO Demand Function, use ARC analysis:

Production Function: Q = F(K,L)where K is Capital and L is Labor.- Generally capital is fixed in the short run, although it is possible for either factor to remain fixedTotal Product: The maximum output produced with given amounts of inputsAverage Product of an Input: measure of output produced per unit of input.Average Product of Labor: APL= Q/L(output of an average worker)Average Product of Capital:APk= Q/K(output per unit of capital)Marginal Product of an Input: change in total output attributable to the last unit of an input.Marginal Product of Labor: MPL = ΔQ/ΔL (output produced by the last worker)Marginal Product of Capital:

MPk = ΔQ/ΔK (output produced by the last unit of capital)Diminishing Marginal Returns: The point where a variable input increases and MP decreases (NOT the same as negative returns)

As the usage of an input increases, marginal product initially increases (increasing marginal returns), then begins to decline (decreasing marginal returns), and eventually becomes negative (negative marginal returns).

Short Run Optimization: When labor or capital vary in the short run, to maximize profit a manager will hire: Labor until :VMPL = w, where VMPL = P x MPL

ORCapital until: VMPK = r, where VMPK = P x MPK

(You want the value of the additional unit = the cost of it)- In the long run both inputs vary

Marginal Rate of Technical Substitution: The rate at which two inputs are substituted while maintaining the same output level. MRTS = MPL/MPK

Isoquant: Illustrates the long-run combinations of inputs (K, L) that yield the producer the same level of output.

- They have diminishing MRTS (negative slope).- They are NON-linear so MRTS will be different at different points.

Isocost: The combinations of inputs that produce a given level of output at the same cost .C = wL + rKK = (1/r)C – (w/r)L

For given input prices, isocosts farther from the origin are associated with higher costs.

Changes in input prices change the slope of the isocost line.Cost Minimization EQ: Where the slope of the isocost line = slope of the isoquant

rw

MPMP

rMP

wMP

K

LKL

rwMRTSKL

Cost Analysis:C(Q) = VC(Q) + FCSunk Cost: A cost that is forever lost after it has been paid.Fixed Costs (FC):Costs that do not change as output changes.

ATC = AVC + AFCATC = C(Q)/QAVC = VC(Q)/QAFC = FC/QMC = DC/DQEconomies of Scale: Occur when long-run average cost decreases as output increasesDiseconomies of scale: Occur when long-run average cost increases as output increases.Constant economies of scale: Occur when long-run average cost remains constant as output increases. Long Run AC:

Multi-Product Cost Function: 2

2212121, cQbQQaQfQQC

Perfect Competition:- Large number of firms- Each firm produces only a very small portion of total market or industry output - All firms produce a homogenous product- Entry into and exit from the market is unrestrictedMonopoly:- One firm produces the entire market output- Strong barriers to entry existMonopolistic Competition:- Large number of firms- Each firm produces only a very small portion of total market or industry output.- Products are close, but not perfect, substitutes.- Entry into and exit from the market is easy.- Firms deliver varying levels of support and service to customersOligopoly:- Few firms produce most or all of total market output.- Products are close or perfect substitutes.- Strong barriers to entry exist- Non-price competition is an important means of competition.Herfindahl Index: HHI = ∑ Si

2

Concentration Ratio: (∑firms shares/number of firms)HHI close to 10,000 = oligopoly or monopoly. (Concentrated)HHI close to 0 = perfect competition or monopolistic competition (Very competitive).HHI = 10,000 ∑ wi

2

where wi= Si /ST

Challenged if HHI >1800 (2500 now) or merger increases HHI by 100 (200 now)However, the government will allow the merger if it achieves an efficiency.