Managerial Economics in a Global Economy

Managerial Economicsin a Global Economy Chapter 3 DEMAND THEORY

The Market Demand Curve Shows the total quantity of the good that would be purchased at each price. Industry and Firm Demand Functions e.g., the demand for computers: Q = b1P + b2I + b3S + B4A; P = price of personal computers I = per capita disposable income S = price of software A = advertising It is necessary to obtain numerical estimates of the b’s (parameters) of the demand function. e.g., Q = -700P + 200I -500S + 0.01A;

Interpretation: one KD  in the price of computers  700 units decrease in the quantity demanded ... etc. Suppose that I = 13000, S = 400, A = 50 000 000 the market demand curve will be Q = -700P + 200(13000) - 0.01(50 000 000) Hence Q = 29 000 000 – 700P; and; P = 4143 - 0.001429Q; (the inverse demand function) • shits in the demand: Suppose that the price of software falls from 400 to 200 Q = 3 000 000 - 700P; and P = 4286 - 0.001429Q;

The Price Elasticity of Demand The sensitivity of quantity demanded to price (measured by the percentage in quantity demanded resulting from a 1 percent change in price) more precisely: e.g.,  = 1.3 (note the sign is not negative) a 1%  in the price of computers  1.3%  in the quantity demanded. Point and Arc Elasticities - Point elasticity e.g., P Q 3 50 4 40 5 3  changes according to the values of P and Q.

Look at the following calculations of point elasticity: •  = (40-30)/30)/((4-5)/5) = 61.67 •  = (30-40)/40)/((5-4)/4) = 61.67 = 3.67 • There is a large difference between the two elasticities even though we used the same data. To avoid this difficulty we use the ARC ELASTICITY OF DEMAND. • Hence;

Using the demand function to calculate the price elasticity Q = -700P + 200I -500S + 0.01A; or Q = 2 900 000 - 700P if P = 3000; Q = 2 900 000 - 700(3000) = 800 000 then calculate: • = -700 • Hence: • if the price falls to 2000; Q = 1 500 000 and

The Income Elasticity of Demand The percentage change in quantity demanded resulting from a 1% change in consumer’s income. • If > 0 Normal goods • [ > 1 for luxury goods] • [ < 1 for necessary goods ] • If < 0 Inferior goods • Calculation of Income Elasticity of Demand e.g.; if Qx = 1000 - 0.2Px + 0.5PY + 0.04I;

= 0.04 I/Q. If I = 10 000 and Q = 1 700 Then: = 0.04(10 000/1 700) = 0.24 ( interpretation ) • Cross Elasticities of Demand Goods can be substitutes (fish and meat and poultry) or complements (cars and petrol) The cross elasticity of demand is defined as the percentage change in the quantity demanded of good X resulting from a 1% change in the price of good Y.

if > 0 goods X and Y are classified as substitutes. < 0 goods X and Y are classified as complements e.g., Qx = 1000 - 0.2Px + 0.5PY + 0.04I; 0.5 . PY/QX if PY = 500 and QX = 1,500 = 0.5 ( 500/1,500 ) 0.17 (Interpretation) • Advertising Elasticity of Demand e.g., (PERFUMES). The percentage change in the quantity demanded resulting from a 1% change in advertising expenditures.

e.g., • Q = 500 - 0.5P + 0.01I + 0.82A; • = 0.82 . A/Q; • if A/Q = KD 2 • = 0.82(2) = 1.64; • The Constant Elasticity Demand Function Given: Q = aP-b1 Ib2 ( non-linear ) if a = 200, b1 = 0.3, b2 = 2; Q = 200P-0.3 I2 ; Note that the price elasticity of demand equals b1 (0.3) irrespective of the value of P or I.

Prove. • Q = aP-b1 Ib2 • differentiate Q with respect to P; = • [note = • substitute for Q = • Hence: [the price elasticity of demand (constant)]

Similarly = = • Hence [the income elasticity of demand (constant)] • the multiplicative demand function can be transformed into linear; • take the logarithms of both sides • log Q = log a - b1 log P + b2 log I;

Using Elasticities in Managerial Decision Making. Some factors that affect the demand are under the control of the firm, others are not. The firm can estimate the elasticity of demand with respect to all the variables that affect the demand, to determine the operational policies to respond to policies of competing firms. e.g. if cross elasticity is high, immediate response. If low less urgent needs to respond. e.g.; Suppose that the demand for coffee X is estimated using the following regression equation: Qx = 1.5 - 3.0Px - 0.8I + 2.0Py - 0.6Ps + 1.2A Ps = the price of sugar, Py = the price of coffee Y. A= advertising

Suppose that this year’s Px = 2, I = 2.5, Py = 1.8 and A=1 Hence: Qx = 1.5 -3(2) + 0.8(2.5) + 2(1.8) - 0.6(0.5) +1.2(1) = 2 This means that this year’s sales are 2 million pounds of coffee. using these information we can calculate various elasticities. Ep = -3(2/2) = -3 EI = 0.8(2.5/2) 1 EXY = 2(1.8/2) = 1.8 EXS = -0.6(0.5/2) = -0.15 EA = 1.1(1/2) = 0.6

We can use these elasticities to forecast the demand for its brand of coffee next year. e.g.; Suppose that the firm intends to: • Px by 5% and  A by 12%. it also expects : • I by 4%,  Py by 7%, and  Ps by 8%. using estimates of elasticities we can determine sales next year as follows: Qx = Qx + Qx(Px/Px)Ep + Qx(I/I)EI + Qx(Py/Py)EXY + Qx(Ps/Px)EXS + Qx(A/A)EA; = 2 + 2(5%)(-3) + 2(4%)(1) + 2(7%)(1.8) + 2(-8%)(-0.15) + 2(12%)(0.6) = 2.2. An increase of 10%

Managerial Economics in a Global Economy