Managerial economics

We will not discuss Demand Forecasting till much later in the semester. So ignore the discussion on forecasting for now and concentrate on the theory of demand.

Handout 4: Demand theory and demand forecasting

Demand is the total quantity of a goods or services that customers are willing and able to purchase at a given price.

Determinants of Demand: Q_X = f(P_X, Prices of related goods, expectations of price changes, population, consumers' incomes, tastes and preferences, advertising expenditures, ...)

e.g., Q_X = a + b₁P_x + b₂P_y + b₃Y + b₄POP + b₅A

The graphical relation between price and the quantity demanded, holding all else constant, is called the Demand curve.

Supply is the total quantity offered for sale.

Factors that influence supply: price of the good, price of related goods, technology, changes in input prices, weather ...

The graphical relation between price and the quantity supplied, holding all else constant, is called the supply curve.

To estimate the demand function,

(1) Specify a model (theory helps determine which data might be important);

(2) Collect data;

(3) Specify an econometric model (e.g., linear, quadratic, inverse, log);

Ex. Quadratic model: Q = a + b₁P + b₂P² + b₃I

Ex. If the model is Q=aP^b1I^b2, estimate

logQ = loga + b₁logP + b₂logI

Then, transform back to original model.

(4) Estimate the model, check the signs of the coefficients and evaluate the significance of the calculated parameters.

Suppose the market demand for good Q_i is specified as Q_i(P_i, P_j, I, Taste) and takes the following form:

Q_i = a - b₁P_i + b₂P_j + b₃I + b₄Taste

If P_j, I and Taste are held constant, then the demand curve is

Q_i = a - bP_i

If price changes, quantity demanded will change -- that is a movement along the demand curve. When any of the other factors that influence demand change, the demand curve shifts.

Basis for Demand: Consumer Theory

Utility maximization

Consider the budget constraint P₁Q₁ + P₂Q₂ = I.

Combinations of goods that provide the same level of utility are called _______________.

Higher indifference curves represent higher levels of utility.

Suppose a consumer chooses a bundle of goods to maximize utility subject to his or her budget constraint.

Ex. Maximize U(Q₁, Q₂) = (Q₁Q₂) subject to P₁Q₁ + P₂Q₂ = I.

L = (Q₁Q₂) + (P₁Q₁ + P₂Q₂ - I)

The first order conditions are

Q₁ = I/2P₁ Q₂ = I/2P₂

Effects of a change in price

Substitution effect: A decrease in P₁ increases the opportunity cost of Q₂, and there is a tendency to substitute Q₁ for Q₂. This is the substitution effect, and it tends to cause the demand for Q₁ to increase when P₁ decreases. It comes about because the decrease in P₁ reduces the price of Q₁ in terms of Q₂.

Income effect: A decrease in P₁ makes it easier to achieve a given bundle of consumption. It is not necessary to spend as much to attain any given level of consumption. If Q₁ is a normal good, then an increase in real income increases Q₁. This is the income effect, which arises because the price decrease raises real income.

The two effects may work in the same or opposite directions depending on the consumer's preferences.

Demand functions

Ex. If a consumer maximizes U(Q₁, Q₂) = Q₁Q₂ + Q₁ + Q₂ subject to the budget constraint P₁Q₁ + P₂Q₂ = I, show that the demand functions are

Q₁ = {I - P₁ + P₂}/2P₁ and Q₂ = {I + P₁ - P₂}/2P₂.

Ex. In the example above, assume the market is composed of two identical consumers denoted i = 1,2.

Consumer i's demand for good 1 is Q_1,i = {I - P₁ + P₂}/2P₁

The aggregate demand for Q₁ is Q_1,market = Q_1,1 + Q_1,2 = {I - P₁ + P₂}/P₁

The ____________________ for a commodity is the horizontal summation of the demand curves of all the consumers in the market.

Graphically, when individual demand curves are summed to get the market demand curve, the aggregate demand curve becomes flatter.

Ex. In the example above, assume the market is composed of N identical consumers. Then, the aggregate demand for Q₁ is

Q_1,market = _i=1^N Q_1,i = _i=1^N {I - P₁ + P₂}/2P₁ =

= f(P₁, P₂, I, N)

Ex. If there are j related goods and N consumers, the market demand for Q₁ is the summation of all the individuals' demands.

Q_1,market = _i=1^N Q_1,i(P₁, P₂, ..., P_j, I)

= f(P₁, P₂, ..., P_j, I, N)

A market in which there is only one consumer is called a _______________.

Properties of demand functions

Suppose the demand for good 1 is a function of its own price, the price of another good and income. The demand for good 1 can be expressed as follows:

Q₁ = f(P₁, P₂, I)

1. If Q_i/I > 0, then good Q_i is a _______________. If Q/I < 0, the good is an _______________.

Examples of inferior goods:

2. If Q_i/P_i < 0, the ____________________. If Q_i/P_i > 0, the good is a _______________.

A Giffen good must be an inferior good. But not all inferior goods are Giffen goods.

Example of Giffen good:

3. If Q_i/P_j > 0, the goods Q_i and Q_j are _______________. If Q_i/P_j < 0, the goods are _______________.

Examples of substitute goods: coffee and tea, beef and pork (substitutes are not consumed together).

Examples of complements: tires and cars (complements are consumed together).

Elasticities of demand

Own-price elasticity of demand: Epsilon = (dQ/dP)*(P/Q)

Ex. If a firm is operating at equilibrium price of P=$75 and quantity Q=5 units along a demand curve P_D= -5Q+100, what is the price elasticity of demand?

Recall that Total Revenue = TR = PQ. Taking the partial derivative with respect to P yields

dTR/dP = d(PQ)/dP = Q + (dQ/dP)P = Q[1 + (dQ/dP)(P/Q)] = Q[1 - |E_p|] Therefore, dTR/dP = Q[1 - |E_p|]

With a increase (decrease) in price, total revenue

1. decreases (increases) if demand is elastic (i.e., |E_p| > 1)

2. remains unchanged if demand is unitary elastic (i.e., |E_p|=1)

3. increases (decreases) if demand is inelastic (i.e., |E_p|<1)

Ex. For heroin, |E_p| = .14. Is the demand for heroin elastic or inelastic? If the price increases due to increased law enforcement, will a heroin dealer's total revenue increase or decrease?

Ex. For marijuana, |E_p| = 1.2. Is the demand for marijuana elastic or inelastic? If the price increases due to increased law enforcement, will a marijuana dealer's total revenue increase or decrease?

Factors which determine price elasticity of demand: Primarily the availability the substitures. The more substitutes there are the greater is the elasticity of demand.

Income elasticity of demand: Epsilon_I=(dQ/dI)*(I/q)

If E_I>0 (because Q/I > 0), the good is __________ good.

If E_I is positive but low, the good is a __________ (e.g., clothes, food).

If E_I is positive and large, the good is a __________ (e.g., yacht, airline travel).

If E_I <0 (because Q/I <0), the good is an __________ good (e.g., pork and beans).

Ex. If Q₁ = I/2P₁, what is the elasticity of demand for Q₁ with respect to income?

E_I =

Is Q₁ a normal good?

Cross-price elasticity of demand Epsilon_XY=(dQ_X/dp_Y)*P_Y/Q_X

If E_XY > 0, commodities X and Y are _______________.

If E_XY < 0, commodities X and Y are _______________.

Ex.: The following is data on income, prices and demand for goods X and Y.

Period Income P_X Q_X P_Y Q_Y

1 $10,000 $25 10 $10 42

2 10,000 28 9 10 40

3 10,000 28 8 15 35

4 11,000 28 9 15 36

5 11,500 34 7 20 32

Calculate the following elasticities (using arc formulas).

A. Between periods 1 and 2, the price elasticity for x is

E_p =

Does the law of demand hold?

B. Between periods 3 and 4, the income elasticity for x is

E_I =

Is the good a normal or inferior good?

C. Between periods 2 and 3, the cross elasticity of demand for X with respect to the price of Y is

E_XY =

Are X and Y substitutes or complements?

Why should no elasticities be calculated between periods 4 and 5?

For the following quotations, indicate the relevant elasticity concept (price elasticity of demand or supply, income elasticity, cross elasticity, etc.) and interpret each quotation:

A. "Economic recovery spurs airline reservations."

B. "The cost of TV commercials prompts cutbacks by advertisers."

C. "Compaq's price cuts on PCs hurts IBM."

Ex. 1 Suppose that Greedy Gary, the manager of the marketing division of Honda, estimated the following regression equation for Honda motorcycles in the New Brunswick area:

Q_H = 1,000 - 10P_H + 0.5N + 5I + 3P_Y - 100P_G + .75A

where Q_H = quantity of Honda motorcycles demanded per year

P_H = price of Honda motorcycles, in dollars

N = number of people between the ages of 20 and 50 living in the New Brunswick area

I = per capita disposable income, in dollars

P_Y = price of Yamaha motorcycles, in dollars

P_G = real price of gasoline, in cents per gallon

A = advertising expenditures by Honda, in dollars per year

A. Find the quantity of Honda motorcycles demanded if the average value of P_H = $9,000, N = 20,000, I = $10,000, P_Y = $5,000, P_G = 105 cents/gallon, and A = $40,000.

B. Derive the equation for the demand curve for Honda motorcycles in the New Brunswick area using the average values for N, I, P_Y, P_G and A.

C. Is quantity demanded sensitive to its "own" price? If so, what will happen to Q_H if P_H increases by $20?

D. Would you expect the demand for Honda motorcycles in the New Brunswick area to be procyclical (i.e. when the economy improves, demand increases) or countercyclical (i.e. demand increases when the economy declines)? Explain your answer.

E. Calculate and interpret the relevant advertising elasticity.

F. If Honda increases its advertising expenditure by 10%, what effect would this have on the quantity demanded?

G. Based on the above information, what would you conclude about consumer preferences for Honda motorcycles over Yamahas? Explain your answer.