QUESTIONS. (a) Calculate the price elasticity of demand when price is Ksh. 2 and when price is

Transcription

1 QUESTIONS NUMBER ONE Given the following demand function Q X = 100 2P 2 (a) Calculate the price elasticity of demand when price is Ksh. 2 and when price is Ksh. 6 (8 marks) (b) Calculate the price elasticity of demand in the price range Ksh. 3 and Ksh. 5 (5marks) (c) If the current prevailing price is Ksh. 5 what advice would you give to the producer in order to increase his revenue, and why? (7 marks) NUMBER TWO (a) Define marginal utility and clearly explain the oxiom of diminishing marginal utility. (6 marks) (b) Illustrate and explain the following: (i) Consumer equilibrium under the cardinalist approach (7 marks) (ii) Consumer equilibrium under the ordinalist approach (7 marks) (Total: 20 marks)

2 ANSWERS NUMBER ONE (a) Calculation of price elasticity of demand when price is 2 and when price is 6: Demand function: Q X = 100 2P 2 Point elasticity of demand as follows: Pεd = Q X P X When P X = 6 P X Q X Q X = -4(6) = -24 Q X = -4P P X P X Q X = 100 2(6) 2 when P X = (6) 2 Q X = -4(2) = -8 (100 72) = 28 units P X Ped = (-24 x 6/28) = Q X = 100 2(2) 2 Ped = 5.14 > 1: (highly) elastic 100 2(4) (100 8) = 92 Units Pεd = (-8 x 2/92) = -16/92 = -4/23 = Pεd = 0.17 < 1 : Inelastic (b) Calculation of the price elasticity of demand in the price range 3 and 5: - Arc elasticity of demand as follows: Arc εd = Q X P 1 + P 2 P X Q 1 + Q 2 When P = 3 Q X = 100 2(3) (9) (100 18) = 82 units

3 when P = 5 Q X = 100 2(5) (25) (100 50) = 50 units Demand schedule P X Q X Q X = (82 50) = (32) P X Arc εd = ( 8) = -128 = = Arc εd = 0.97<1: inelastic (c) Pεd = Q X P X P X Q X Q X = P 2 Where P X = 5, Q X = 50 Q X = -4P = -20 at P = 5 P X Pεd = (-20 x 5/50) = -2 Pεd = 2 > 1 : price elastic demand Advice:

4 The demand for commodity X is (price) elastic implying that any change in price causes a more than proportionate change in quantity demanded (and revenue from sales which is the product of the price and quantity of X purchased). An increase in price of commodity X, in this case, will more than proportionately reduce the quantity demanded and revenue; a fall in price would more than proportionately increase the quantity demanded and revenue from sales. Accordingly therefore, since the producer of commodity X seeks to maximize sales (and profits) it would be very much advisable to either reduce the price or maintain it stable at 5 but NOT increasing it above 5. A diagram can also be used to clearly demonstrate to the producer the impact of a price change on sales revenue where demand is price elastic.

5 P X Where P 1 = 5 P 1 D P 2 D 0 Q 1 Q 2 Qd X Fig 13.1: elastic demand curve for commodity X NUMBER TWO (a) Marginal utility is the additional satisfaction derived from the consumption of an extra unit of a commodity. It is measured by the derivative of the total utility function, that is, change in total utility per unit change in the quantity (of a commodity) consumed: MU = dtu/dq where MU: Marginal utility TU: Total utility Q: Quantity consumed. This additional satisfaction (marginal utility) decreases as successive units of a commodity are consumed thus diminishing marginal utility. Marginal utility falls under the cardinalist approach of consumer behaviour which assumes that consumer satisfaction (utility) is measurable in terms of money the consumer is willing and able to pay for a commodity. Marginal utility varies from one individual to another e.g. a person in North Eastern province of Kenya will find a glass of cold juice very satisfying relative to a person in a cold area like Limuru or Kericho. Diminishing marginal utility is based on the following assumptions: Utility is measurable Constant marginal utility of money

6 Normality of goods and rationality of the consumer Successive units are homogenous Continuity in consumption of the successive units. When marginal utility is greater than zero, total utility is rising; total utility is maximum when marginal utility is zero; when marginal utility is less than zero (- ve) the total utility falls. Therefore, total utility (TU) increases at a decreasing rate since marginal utility (mu) decreases at all levels of subsequent consumption of successive units of a commodity. Assuming consumption of one commodity, the consumer would be in equilibrium when the marginal utility of the commodity is equal to the price of the commodity i.e. Mu X = P X where X is the commodity consumed. Where more than one commodity is consumed (purchased) then the consumer would be in equilibrium at the point where the marginal utility per shilling spent on each product is the same (i.e. the point of equi-marginal utility): MUx/Px = MUy/Py =MUn/Pn Where X: Commodity X Y: Commodity Y n: Commodity n Marginal Utility (MU X ) 0 X 1 Units of X(Q X ) MU Fig 14.1: Diminishing Marginal Utility

7 Units of commodity X (Q X ) Total Utility (TU X ) Marginal Utility (MU X ) (b)(i) Consumer equilibrium under the cardinalist approach: The cardinalist approach of consumer theory assumes measurable utility in monetary terms such that the consumer is in equilibrium when marginal utility derived from the consumption of a commodity is equal to the unit price of the commodity, that is, MU X = Px. Where there are more than one commodities, the condition for the equilibrium of the consumer is the equality of the ratios of the marginal utilities of the respective commodities to their prices i.e. MU X = MU Y = MUn P X P Y Pn The marginal utility per shilling spent on all commodities is the same. Assuming one commodity (X), a fall in price distorts the equilibrium of the consumer which becomes Mux>Px; to go back to equilibrium the consumer should reduce the marginal utility of X by consuming more of X pursuant to the oxiom of diminishing marginal utility. Assuming commodities X and Y, consumer equilibrium is attained where MU X = MU Y : where MUx & MUy: marginal utilities of commodities X and Y P X P Y respectively. Px & Py : Prices of commodities X and Y respectively.

8 If for instance, the price of X falls, Mux/Px>Muy/Py and to go back to equilibrium, Muy should be increased by consuming less of commodity Y or increasing the consumption of X in order to reduce Mux again pursuant to the law of diminishing marginal utility. Therefore, as the price of a commodity (x) increases, the consumer s marginal utility falls such that the consumer is now willing and able to purchase relatively less units of X (in order to increase utility) thereby reducing the quantity demanded of commodity X. If however, the price of X falls, Mux increases and therefore the consumer would be willing and able to buy more of X hence increasing the quantity demanded of X. Thus a normal demand curve is based on the law of diminishing marginal utility. (ii) Consumer equilibrium under the ordinalist approach: Consumer equilibrium refers to a specific point in consumption of (two) goods from which the consumer derives maximum satisfaction subject to a given budget constraint (determined by the consumer s income and commodity prices). This equilibrium point is achieved at the point of tangency of a budget line to the highest possible indifference curve; at this point, the slope of the indifference curve (i.e. marginal rate of substitution MRS) is equal to the slope of the budget line (i.e. relative commodity prices) Thus, at equilibrium MRSxy = Px/Py. Indifference curve defined as the locus of possible combinations of two commodities their consumption from which the consumer derives the same level of satisfaction. Such curves are negatively sloped, do not intersect and convex to the origin. Budget line refers to the locus of combinations of two goods whose purchase exhausts the consumer s budget constraint (money outlay). Units of Commodity Y Units of Y A I/P Y

9 I I/P X 0 Units of Commodity X 0 B Units of X Fig 14.2: Indifference Curve Fig: 14.3: Budget line At the point of tangency, the consumer is said to be in equilibrium as shown below:

10 Units of Commodity Y A Ye e B 0 Xe Units of Commodity X Fig : 14.4: Consumer equilibrium Point (e) is consumer equilibrium point where the slope of the budget line (AB) (Px/Py) is equal to the slope of the indifference curve (I 2 ) (MRS XY ) with X e of X and Y e of Y. The indifference curve (I 2 ) has its maximum convexity at point (e) denoting diminishing marginal rate of substitution. The indifference curve (I 1 ) is attainable but inefficient since it does not maximize satisfaction, that is, consumer s income is not fully utilized. Similarly, indifference curve (I 3 ) is NOT attainable with the present level of income and commodity prices. It is therefore at the point of tangency (e) that the consumer maximizes satisfaction by fully spending the disposable income on Xe of X and Ye of commodity Y, given the prices of X and Y. I 1 I 2 I 3