Managerial Economics Final

IntroductionEconomics – Branches: Micro- and Macro-Economics, from micro- to managerial economics or economics of firm.Key Concepts: Demand and Supply sides of economic units and aggregates – optimization.Laws of Demand and Supply, exception of Law of Demand; equilibrium price and quantity.

Show demand and supply curves and the equilibrium

Issues and Importance of Study of Managerial Economics

Managerial Economics is “the application of economics to the real business activities so as to get desired business results” in a fiercely competitive environment where thousands of rivals plan strategies to get control of the market.

Important Issues: Production, cost and organization of firms in market place.Topics studied: • Law of demand and elasticity of demand• Demand forecasting• Production theory – returns to scale, technology, cost,

revenue and profit• Objectives of firms• Determination of prices– methods, cartels, groups,

leadership• Tools to judge economic efficiency – break-even analysis,

linear programming, game theory etc• Micro planning – project, capital budgeting, cost benefit

analysis, public investment criteria regarding turnkey projects

• Business environment and social welfare.

Where do Principles of Micro-economics fit in managerial decision making?

The primary activities of decision making are:• Finding occasions for making decisions• Identifying possible courses of action• Evaluating the revenues and costs associated with each course of action• Choosing the course that best meets the goals and objective of the firm, which is maximizing the wealth of a

firm PV of net cash flows or PV (π) and PV (π) = π1/(1+r) + π2/(1+r)

2 + π3/(1+r)3 + …….+ πn/(1+r)

n

Where, πn is the profit in year n in current prices and r is an appropriate discount rate for converting future value into present value.

Constraints to Decision MakingConstraints in managerial decision making involve:• Legal - including environmental laws, laws relating

to women’s/child rights, provisions inconsistent with generally accepted standards of behavior

• Contractual – bind the firm because of some prir agreements

• Financial – maximize production subject to the budgeted amount

• Technological considerations – set physical limit on capacity/volume of production

Circular Flow of Economic Activities

Payment for goods/service Payment for Goods/Services

Product Market

Goods and Services Goods and Services

Households

Economic Resources

Firms

Income

Factor Market Factor Payments

Economic Resources

Demand Analysis

Individual and Market demand: Definition/explanation.Illustration: Max, a graduating senior has accumulated an impressive

file of tests during his college career. He plans to sell the collection to three prospective buyers, whose demand equations are: Q1 = 30 – 3P, Q2 = 22.5 – 0.75P, and Q3 = 37.5 – 1.25P, where, Q1, Q2 and Q3 are quantity demanded by the three buyers. Calculate (a) the demand equation for Max’s tests (b) how many more tests he can sell for each one-dollar decrease in price, (c) the charge to sell his entire collection if he has a file of 60 tests and (d) the quantity demanded by each of the three buyers at this price

(a) Market demand Qm = Q1+ Q2 + Q3

=30 – 3P + 22.5 – 0.75P + 37.5 – 1.25P = 90 – 3P(b) The equation shows that an 1 dollar decrease in price will increase

the quantity demanded by 3 tests(c) To sell the entire set of collections, i.e., Qm = 60, Qm = 90 – 3P or, 60 = 90 - 3p, which makes P = 10 and (d) at price P = 10, Q1 = 30 – 10 = 20 tests; Q2 = 22.5 – 0.75 x10 = 15 tests and Q3 = 37.5 – 1.25 x 10 = 25 tests

Demand, Supply and Equilibrium

Demand Function Qd = a + bP, where b<0 and

Qs = c + dP, where d >0

At equilibrium, Qd = Qs => a + bP = c + dP

Which implies Pe = c – a/b – d

and Qe= a + b (c – a/b – d)

Specific case: Qd = 14 – 2P and Qs = 2 + 4P

At equilibrium, Qd = Qs => 14 – 2P = 2 + 4P

Solving the equations, we get Pe = 2 and Qe=10 units

Theory of Costs

Involves three important/basic areas of managerial economics:• Resource allocation decisions;• Decisions on expanding product line;• Decisions on capital investment; there are other areasExplicit cost – actual payments to other parties, also called

accounting costImplicit cost – value of foregone opportunities but do not involve

an actual cash payment Sunk cost – Expenditures made in the past or to be made in future

against contractual arrangement. Example: cost of inventory, future rental payments on a warehouse (as part of long-term lease)

Marginal cost – cost associated with a one-unit change in the output

Incremental cost – total additional cost of implementing a managerial decision; Example – cost of adding a new product line, acquiring a major competitor, developing an in-house legal staff etc.

Opportunity cost – value of next best alternative foregone

Fixed Cost, Variable Cost and Marginal CostCapital Labor

InputOutput Rate

TFC AFC TVC AVC Total Cost

Marginal Cost

10 0 0 1000 ─ 0 ─ 1000 ─10 2 1 1000 1000 200 200 1200 20010 3.67 2 1000 500 367 184 1367 16710 5.1 3 1000 333 510 170 1510 14310 6.77 4 1000 250 677 169 1677 16710 8.77 5 1000 200 877 175 1877 20010 11.27 6 1000 167 1127 188 2127 25010 14.60 7 1000 143 1460 208 2460 33310 24.60 8 1000 125 2460 307 3460 1000

Draw curves for TFC, TVC, TC, MC, AC, AVC by using the above data; MC, AC and AVC first decline, reach a minimum and then shift upwards; short-run cost curves are U-shaped, long-run cost curves are flatter.

Costs and the Concept of Profit-1

Total cost (TC), fixed cost (FC), variable cost (VC), average cost (c/q), marginal

cost (Δc/Δq; m in y = mx + c) accounting cost, explicit cost, implicit cost,

economic cost (explicit + implicit cost),opportunity cost; revenue and break-even analysis

Calculation of Economic Profit Econ. Profit =Sales $90,000 Revues minus all

Less: Cost of goods sold $40,000 relevant costs,Gross profit $50,000 both explicit and

Less: Advertising $10,000 implicit Depreciation $10,000 Utilities $3,000 Property Tax $2,000 Misc. expenses $5,000

$30,000Net Accounting Profit $20,000Less: Implicit Costs

Return on own capital invested $10,000 Opportunity cost ($5000 x 12) $60,000

$70,000

Net Economic Profit ─$50,000[Net accounting profit – implicit costs]

Costs and the Concept of Profit-2Suppose that you are a good dressmaker. You have 4

yards of a material purchased for Tk 200 per yard a few years ago. You gave the options for (a) selling it now @Tk 1200 per yard and (b) using it in making dress that may sell for Tk 7200. The making of the dress would require 4 hours of your labor, which you can sell elsewhere for Tk 800 per hour. Decide whether you should make the dress or sell the material.

Soln: Revenue from sale of the material Tk 7200Less: cost of the material 4 x 1200 = 4800

4 hors of labor 4 x 800 = 3200 8000

Economic Profit Tk.– 800 Alternatively, if economic cost is not consideredRevenue = Tk 7200 and, considering the historical

value only, Material cost = 4 x 400 = Tk 1600 Profit = 7200 – 1600 = Tk 5600

Cost, Revenue, Profit and Firm’s Equilibrium-1Total cost function C = 1000 + 10q – 0.9q2 + 0.04q3

MC = dc/dq = 10 – 1.8q + 0.12q2

Total variable cost = Total cost – fixed cost = 10q – 0.9q2 + 0.04q3

AVC = TVC/q = 10 – 0.9q + 0.04q2

Profit π = Revenue – Cost = pq – (FC + q.AVC)Or, π + FC = q(p – AVC) => q = (FC + π)/(p – AVC)

This gives the rate of output necessary to generate a certain amount of profit π

At break-even the π = 0 and therefore, the break-even volume of output is qBE = FC/(p – AVC)

Cost, Revenue, Profit and Firm’s Equilibrium-2Example: FC of a firm is $10000, price per unit of its

product is $20 and AVC (MC) of the form’s product is $15. The firm has a target for a profit of $20000. The volume of output required to achieve the target is:

q = (FC + π)/(p – AVC) = (10000 + 20000)/(20 – 15) = 6000 units

Reminder: The break-even output can be obtained from the

equation by taking π = 0 i.e., the break-even volume of output for the above firm would be

FC /(p – AVC) = 10000 /(20 – 15) = 2000 units

Show the graphs for FC, VC, TC, TR and the BE value

Optimization of a Firm’s OutputFollowing are the cost and revenue functions for a firm:TC = 50 + 4q and TR = 20q ─ q2; Calculate the volume of output for which profit would be maximum.Profit π = (20q ─ q2) − (50 + 4q) = 16q – q2 – 50dπ/dq = 16 – 2q dπ/dq = 0 => 16 – 2q => q = 8 ………(i) and d/dq(dπ/dq )= – 2 < 0 ...……(ii)Conditions (i) and (ii) indicate that the firm will havemaximum profit if the output is 8 units and the profit at output 8 is: π8 = 16q – q2 – 50 = 16x8 – 82 – 50 = 30 unitsAlternatively,MC = dc/dq = 4 and MR = dπ/dq = 20 – 2q and For πmax MC = MR => 4 = 20 – 2q i.e., q = 8 implying that profit is maximum when q = 8 units.

Consumer Behavior

Consumer’s equilibrium (maximization of satisfaction)Utility (total and marginal, and Marginal Utility Theoryto explain consumer’s equilibrium: TU and MUSchedule; MU diminishes, TU is maximum when MUis zero, and consumer is in equilibrium when MU = 0.

Indifference Curve Theory: indifference, indifferenceschedule and curve, properties of indifference curve, budget line, consumer’s equilibrium on the indifference curve, shifts in consumer’s equilibriumbased on changes in price and income (PCC and ICC)

Elasticity of DemandElasticity = measure for response in demand to

change in price and income; price, income, cross and substitution elasticity

Price elasticity of demand ep =(proportionate change in quantity demanded of a

product X) ÷ (proportionate change in price of the product x)

ep = ─(Δq/q)÷ (Δp/p ) = ─ (dq/dp). p/q The price of a product changes from tk 10 per unit to

Tk 12 and because of this, the quantity demanded changes from 10 units to 7 units. The ep stands at ─ 1.5, this means that the increase in price by 1% would cause a reduction in demand by 1.5%.

Let the demand equation is Qd = 100 – 4p i.e., the demand at price $10 is 100 – 4x10 = 60 units and the

ep = ─ (dq/dp). p/q or, – 4. 10/60 = ─ 0.67

Price Elasticity of DemandDeterminants of ep

Availability of substitutes – products having good substitutes have high ep

Proportion of income spent – demand tends to be inelastic for goods and services that account for only a small proportion of total expenditure (demand for salt)

Time period – demands are usually elastic in the long term than in the short run; people have preference in maintaining the standards in consumption once achieved and consumers adjust expenditures in the long run.

ep<–1, the demand is elastic (luxury goods), if price increases, consumers spend less, revenues of sellers decrease

ep = –1, unitary elastic, revenues of sellers remain unchanged

–1< ep<0, demand is inelastic (everyday necessities), revenues of sellers increase, even with increase in price

Income Elasticity of Demand

Income elasticity of demand ei =(proportionate change in quantity demanded of a product X) ÷ (proportionate change in income of the consumer buying it)

ei = (Δq/q)÷ (ΔI/I ) = (dq/dI). I/q Let the demand equation is Qd = 50,000 + 5I. If someone’s

income(I) is Tk 10,500, Qd = 50,000 + 5x10,500 = 102,500; and ei = (dq/dI). I/q = 5. 10,500/50,000 = 0.512This means that the an 1% increase in income causes

0.512% increase in the quantity of a product (for which the ei = 0.512) consumed.Income elasticity is usually positive. But take the case of hot

dogs (in the US) – it is a food for low income group of people. But if the income of this group of people increases, they usually give up hot dogs and switch to other types of meat. Therefore, income elasticity of hot dogs may be negative.

Use of the concept of elasticity: pricing, targeting of products for different market segments

Income elasticity: Engel’s Law

Percentage of income spent on food decreases as income increases – Ernst Engel, Germany

Implication: • Farmers may not prosper as much as people in

other occupations during the periods of economic prosperity;

• Food expenditures do not keep pace with increases in GDP;

• Farm incomes may not increase as rapidly as incomes in general

Cross Elasticity of DemandThe responsiveness of quantity demanded of a product X to change in the price of another (usually, a substitute or complementary) product Yec =(proportionate change in quantity demanded of a

product X) ÷ (proportionate change in price of another product Y)ec = (Δqx/qx)÷ (Δpy/py ) = (dqx/dpy)÷ (py/qx ) A fall in price of a product Y increases demand for its complementary product XReduction in price of a product Y decreases demand for its substitute product X; however, cross elasticity is not reciprocal i.e., ec for coffee is not the same as ec for

tea, tastes of consumers, their incomes, price of some other products matter.Exercise: the demand for X in terms of the price for y is given by qx = 100 + 0.5 py; calculate ec Soln: ec = (dqx/dpy)÷ (py/qx ) = (150 – 125)/(100 - 50)÷ (50 + 100)/(125 + 150) = 0.27; Note: (py/qx ) should be calculated as the ratio

of ranges

Elasticity: Problem

The demand for (Qx) for books of a publishing company is determined as Qx = 12000 – 5000Px + 5I + 500Pc, where

Px = price charged for the company’s books I = per capita income of the buyers Pc= price of the books of competing publishers Determine the effect ofa. increase in price of the company’s books on its

revenuesb. rising incomes of the buyers on the sale of the

company’s booksc. rise in prices of the books of the competing publishers

on the demand for the company’s booksAssume that the initial values of Px, I, and Pc are $5,

$10,000 and $6 respectively

Solution to Elasticity: Problema. Effect of increase in price of the company’s books on its revenuesThe effect of increase in price can be assessed by computing price

elasticity of demand. Substituting the initial values of I and Pc in the demand equation,

Qx = 12000 – 5000Px + 5(10000)I + 500(6) = 65000 – 5000Px The value of dq/dp for the given demand equation is:

dQx/dPx = d/dPx (65000 – 5000Px)= – 5000; and p/q = Px/Qx

where Px = $5 and Qx= 65000 – 5000Px = 65000 – 5000(6) = 40000

Now, ep = ─ (dq/dp). p/q and for the given demand equation

ep = ─ 5000 . 5/40000 = ─ 0.625 [dq/dp= dQx/dPx = ─ 5000, and p/q = Px/Qx where Px = $5 and Qx= 40000]. The value of ep = ─ 0.625 i.e., – 1 < ep < 0 implies that the company’s books are price inelastic and raising the price of its books will increase the total revenue

Solution to Elasticity: Problemb. Income elasticity ei = dQx/dI . I/QThe demand function is: Qx = 12000 – 5000Px + 5I + 500Pc

dQx/dI = 5, and at income I = 10,000 quantity demanded Qx = 40,000 , which means that theincome elasticity ei = dQx/dI . I/Q= 5. 10000/40000 = 1.25

We find that income elasticity ei > 1. this implies that the company’s books belong to luxury goods. Since with increase in income buyers tend to buy more of luxury goods, during the period of rising incomes, the sale of the company’s books will increase.

Solution to Elasticity: Problem

c. The demand function is: Qx = 12000 – 5000Px + 5I + 500PcAnd the cross elasticity ec = dQx/dPy . Py/QxThe Pc in the demand curve is equivalent to Py of the crosselasticity and ec = dQx/dPy.Py/Qx = 500. 6/4000 = 0.075 [since dQx/dPy = dQx/dPc = 500]This implies that a 1% increase in the price of the books of

competing publishers would result in a 0.075% increase in the demand for the company’s books.

Regression EquationSimple regression – relationship between two variablesY = a + bX, where Y may be production cost and X output.Y = dependent variable, X = independent variable, a = intercept on y- axis and in the given case, fixed costb = slope of the cost function, variable cost per unit or

marginal cost; the function may be compared with the equation y = mx + c

Problem: Formulate the regression equation and predict the cost of producing 20 units of the product

Show freehand plotting of the costAt the different levels of output and Draw the straight line cruisingThrough the points.

PRODUCTION PERIOD

TOTAL COST ($Y)

TOTAL OUTPUT (X)

1 100 0

2 150 5

3 160 8

4 240 10

5 230 15

6 370 23

7 410 25

Regression Equation: Soln of the ProblemCost (Yt) Output (Xt) Yt – Yav Xt – Xav (Xt – Xav )2 (Xt – Xav)(Yt – Yav )

100 0 ─ 137.14 ─ 12.29 151.04 1685.45

150 5 ─ 87.14 ─ 7.29 53.14 635.25

160 8 ─ 77.14 ─ 4.29 18.40 330.93

240 10 ─ 2.86 ─ 2.29 5.24 ─ 6.55

230 15 ─ 7.14 2.71 7.34 ─ 19.35

370 23 132.86 10.71 114.70 1422.93

410 25 172.86 12.71 161.54 2197.05

Yav =237.14 Xav = 12.29 Σ(Xt – Xav )2

= 511.40Σ(Xt – Xav)(Yt – Yav )= 6245.71

The regression equation is: Y = a + bX, where, b = Σ(Xt – Xav)(Yt – Yav ) ÷ Σ(Xt – Xav )2 = 6245.71 ÷ 511.40 = 12.21;

a = Yav – bXav = 237.14 – (12.21)(12.29) = 87.08The equation therefore, is Y = 87.08 + 12.21XAdd: talk about R2 – the coefficient of determination (proportion of the dependent variable explained by the regression , value of it varies between 0 and 1; when the value of R2 is higher it means that the regression fits the data very well.

Production Function

Production function relates output to inputs; general equation is: Q = f(K,L), where K is capital and L is labor;one of the specific is the Cobb-Douglas production

function Q = AKαLβ where A, α and β are constants. Prices of inputs and the price of the output must be used

with production to determine which of the possible input combinations is the best give the firm’s objective.

Marginal product: addition to total product for one extra unit of an input and

Marginal product of capital MPk = dQ/dK = αAKα –1Lβ andMarginal product of labor MPL = dQ/dL = βAKαLβ – 1 Law of diminishing marginal return: when increasing

amounts of a variable input are continued with a fixed level of another input, a point will be reached when marginal product of the variable input will decrease.

Matrix of Inputs (capital and labor) and Output CAPITAL↓

8 283 400 490 565 632 693 748 800

7 265 374 458 529 592 648 700 748

6 245 346 424 490 548 600 648 693

5 224 316 387 447 500 548 592 632

4 200 283 346 400 447 490 529 565

3 173 245 300 346 387 424 458 490

2 141 200 245 283 316 346 374 400

1 100 141 173 200 224 245 265 283

Labor→ 1 2 3 4 5 6 7 8

•If 4 units of capital and 2 units of labor are used, the maximum production will be 283 units; if K = 8 and L = 2, the output Q = 400 units , and the like.•There is a substitutability between the factors of production; there are varying ways to produce a particular rate of output by using different combinations of inputs•245 units can be output can be produced by using any of the combinations - K = 6 and L = 1, K = 3 and L = 2, K = 2 and L = 3 or K = 1 and L = 6•A firm can use a labor intensive or a capital intensive process (e.g., 6 units of capital and 1 unit of labor or 1 unit of capital and 6 units of labor to produce the same output.

Total, Average and Marginal ProductsTen equally skilled and diligent workers are ready to work in a

factory equipped with machines and ready stock of materials. As workers add in, the output increases and figures on the number of workers, total product, average product and marginal product can be shown as under:

Av. Product (AP)= average output per unit and AP = TP/L,TP = Total productL = No of workersMarginal Product (MP)= change in outputAssociated with one-Unit change in workersMP = ΔQ/ΔL,Q = amount of output.

No of Workers Total Product Av. Product Marginal Product

0 0 − −

1 2 2 2

2 5 2.5 3

3 9 3 4

4 14 3.5 5

5 22 4.4 8

6 40 6.7 18

7 57 8.1 17

8 63 7.9 6

9 64 7.1 1

10 63 6.3 − 1

Total Output

Total Output (Q)

Rate of labor input (L)

Average and Marginal Product

Marginal product

Average product

Rate of labor input

Producer’s Equilibrium

Output at which a producer is most satisfied, usually, a level at which the firm has the maximum profit, which can be attained either by minimizing costs or maximizing sales. Minimizing costs: manufacturer may use two factors of production and a number of different combinations of the factors can yield the same amount of output. The curve representing these combinations is called the iso-quant/equal product curve/product indifference curve. The producer may choose any of these combinations but his decision on which combination he would pick depends on the prices of the factors and his budget that may be shown by his budget line.

Isoquant

Budget Line

Producer’s EquilibriumMaximizing revenue: The manufacturer has a fixed

amount of resources and he can produce different combination of two goods that may be produced by the same amount of resources. The curve drawn by plotting the points showing such combinations is called production possibility curve and the manufacturer can choose any of these combinations.

But the manufacturers choice will be determined by the market prices of the goods and he will chose the combination that gives him the maximum revenue. The curve that shows the different combinations of two goods that can give the same amount of revenue is called the iso-revenue curve.

Production Iso-revenue possibility curve curve

Returns to ScaleQ = f(K,L), if both inputs are changed by some factor λ output may

change to some factor h, which may be equal to λ, more than λ or less than λ. Now consider the case hQ = f(λk, λL), where λ = 2 i.e., both the inputs are doubled. In such case, the Cobb-Douglas production function Q = AKαLβ may look like

hQ = A(2K)α(2L)β = 2α + β(AKαLβ) = 2α + β(Q) => h = 2α + β

The equation h = 2α + β is derived from a production function that uses both factors K and L increased by 2 times and the equation shows that if both factors of production are increased by 2 times, the output increases by this increases 2α + β times.

If the proportion in which the output increases is the same as the proportion of increase of the inputs i.e., if h = 2 then α + β = 1

This is a situation when we have constant returns to scale. Similarly, if h > 2, α + β > 1, it is a situation, when we have increasing returns to scale and if h < 2, α + β < 1, it is a situation, when we have decreasing returns to scale. Thus in case of constant returns to scale, the function Q = AKαLβ may be written as Q = AKαL1 – α

Economies of Scale

Economies of scale may be understood as the benefits obtained because of increase in the size of the firm/output. Why do increasing returns to scale occur?

• Use of technologies that are cost-efficient at high levels of production

• Specialization of labor• Economies in inventoriesWhen do decreasing returns to scale occur?When firms grow so large that the management cannot

effectively manage (for example, increase in costs of gathering, organizing, transportation, reviewing information etc)

Economies of scope: firms often find that even without increasing the scale, per unit costs are lower when two or more products are produced (because of use of idle/temporarily ‘surplus’ capacity)