# Economics Problems

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17-Jan-2015

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• 1. PROBLEMS Market Demand Analysis: Q1. Construct a demand schedule for a product X for alternative prices Re.1, 2, 3, 4,and 5 given its demand function : Dx = 90 2Px. Draw the demand curve for the same? What is its mathematical attribute? P = 1 .. Dx = 90 2 Px = 90 2 x 1 = 90 2 = 88 P = 2 .. Dx = 90 2 x 2 = 90-4 = 86 P = 3 .. Dx = 90 2 x 3 = 90-6 = 84 P = 4 Dx = 90 8 = 82 P = 5 Dx = 90 10 = 80 Mathematical attribute = Dx = f (Px), Dx < 0 Px Q2. The demand curve for a commodity X is represented by Qx = 160000 1000Px. Construct the demand schedule assuming initial price to be Rs.100 and consequent increase by Rs.10 upto Rs.150. Plot the demand curve. P = 100 Dx = 160000 1000 Px = 160000 - 1000 x 100 = 160000 100000 = 60000 P = 110 Dx = 160000 1000 x 110 = 160000 110000 = 50000 P = 120 Dx = 40000 P = 130 Dx = 30000 P = 140 Dx = 20000 P = 150 Dx = 10000 Q3. Suppose the demand function for Komal butter in a town is estimated to be Qd = 600 5P when Qd is the quantity demanded of butter (in 000 kgs per week) and P stands for price, a) estimate at what price demand would be zero. If Qd = 0 , then 0 = 600 5P, 5P = 600 P = 600/5 = 120. When demand is zero, price is Rs.120. 1
• 2. b) Draw a demand curve at alternative prices Rs.25, 35, 50, 60 and 80. P = 25, Qd = 600 5P = 600 5 x 25 = 600 125 = 475 P = 35, Qd = 600 - 5P = 600 5 x 35 = 600 175 = 425 P = 50 Qd = 600 5 x 50 = 600 250 = 350 P = 60 Qd = 600 5 x 60 = 600 300 = 300 P = 80 Qd = 600 - 5 x 80 = 600 400 = 200 c) What is the statistical characteristics of this demand curve. Downward sloping showing demand steadily falls as price increases. Q4. Central Plaza conducted a study of the demand for mens ties. It found that the average monthly demand (D) in terms of price (P) is given by the equation D = 800 5P. How many ties per day can its store expect to sell at a price of Rs.100 per tie? Demand Equation for ties is Dx = 800 5P. If P = 100 Dx = 800 5 x 100 = 300 Demand is 300 per month, or 10 per day. If the store wants to sell 500 ties per month, what price it should charge? If Dx = 500, 500 = 800 5P, 5P = 800 500 = 300, P = 300/5 = 60. Q5. Demand equation of Sonam tiles is estimated as P = 8000 24Q, Find i) the marginal revenue when Q = 100 and Q = 200 When Q = 100 MR = 8000 24 x 100 = 8000 2400 = 5600 When Q = 200 MR = 8000 24 x 200 = 8000 4800 = 3200 TR is Max. when MR = 0 When MR = 0 8000 24Q = 0 24Q = 8000, Q = 8000/24 = 333 Q6. The demand function for beer in a city is given as Qd = 400 4P, Where Qd = quantity demanded of beer (in 000 bottles per week), P = price of beer per bottle. 2
• 3. a) Construct a demand curve assuming price Rs.10, 12, 15, 20, 25 per bottle. b) At what price would the demand be zero. c) If the producer wants to sell 380,000 bottles per week, what price should he charge? Ans. P = 10 : Qd = 400 4 x 10 = 360 P = 12 : Qd = 400 4 x 12 = 352 P = 15 : Qd = 400 4 x 15 = 340 P = 20 : Qd = 400 4 x 20 = 320 P = 25 : Qd = 400 4 x 25 = 300 a)The data has been plotted on a graph as under : P 25 - 20 - 15 10 0 300 310 320 330 340 350 360 Qd Scale : Y-axis 2 cm 10, For convenience, there is the scale from origin on x-axis. DD is the linear demand curve derived on the basis of the given function and given the alternative prices. b)In the equation : Qd = 400 4P, let us put Qd = 0 400 P = 0 , 4P = 400, P = 100. 3
• 4. That is to say, at the price of Rs.100 per bottle, the demand for beer will be zero. c) 380,000 bottles is 380 (000 omitted) In the given equation Qd = 400 4P, let Qd = 380, 380 = 400 4P, 4P = 400 380 4P = 20, P =5 The producer should fix the price at Rs.5 per bottle, in order to sell 380,000 bottles per week. Q7. Truett and Ruett (1980) described the following demand function for a brand X of microwave ovens : Qx = f (Px, Pz, Nw, Y, A) Where Qx = quantity demanded per year for brand X of microwave ovens in a city, Px = price of X brand Pz = price of Z brand Nw= number of working women Y = mean annual household income A = annual advertising expenditure Assuming hypothetical data, we may state the demand estimation as under : Qx = 11,93,200 100Px + 20 Pz + 0.002 Nw + 1.8Y + 0.3A On this basis, given that Px = 8000, Pz = 9000, Nw = 800,000 in a city, Y = 100,000 A = 60,000 We can estimate the demand for X brand microwave oven as follows: Quantity demanded Qx = 11,93,200 (100 x 8000) + (20 x 9000) + (0.002 x 800,000) + (1.8 x 100,000) + (0.3 x 60,000) = 11,93,200 (800,000 + 180,000 + 1600 + 180,000 + 1800) = 11,93,200 11,63,400 = 29,800 4
• 5. 29,800 microwave ovens of X brand are purchased annually in this city. Case Study Problems: On combined effects of elesticities of demand: Price effect and income effect together on the demand for a particular product can be captured through combined effects of price and income elasticities of demand by using the following equation : Q2 = Q1 [1 + ep (%P) + em (%M) Where Q1 = initial (current period) quantity demanded Q2 = estimated demanded quantity in relation to changes in price and income. P = price M = income ep = price elasticity of demand em = income elasticity of demand. Illustration: Q8(1) Panavision a TV manufacturing company, is planning to increase the price of its television sets by 10 % next year. The economic report of the company has forecast a rise in per capita income by 5% during the period. Panavision economic adviser has estimated price elasticity for the TV set at 1.4 and income elasticity at 2.2. The Panavision currently sells 50,000 TV sets. Give the forecast for the sales. Is it advisable to raise the price of TV sets as has been decided in this case when each TV set is currently priced at Rs,10,000? Solution: Given particulars : Ep = -1.4, em = 2.2 Q1 = 50,000 %P = 10% %M = 5% Q2 = 50,000 [1 + (-1.4(0.10) + (2.2)(0.05)] = 50,000 x 0.97 = 48,500 Thus, positive income effect is more than offset by the negative price effect. As such, sales will decline to 48,500. At initial price of Rs.10,000 annual revenue of the firm is Rs,50 lakhs. When the price is raised to Rs.11,000, 48,500 TV sets are expected to be sold. This would fetch a revenue of 48,500 X 11000 = Rs. 53.35 lakhs. 5
• 6. Thus, the company is going to gain and should, therefore, proceed by its decision. Q9. A number of empirical studies of automobile demand in a country have observed that the price elasticity is approx. -1.2 and the income elasticity is + 2.8. The current sales amount to 8 million units. If the price rises by 10% and income rises 5% next year, how many cars are expected to be sold? Ans. Given price effect on price elasticity ep = - 1.2% Income effect on income elasticity em = 2.8% %Q = ep x P + em x %M = -1.2 x 10% + 2.8 x 5% 1.02 Demand for automobiles = Qa = 1.02 x 8 million = 8.16 million cars. Q2 = Q1[1+ eP (P) + eM(M)] = 8 [1 + -1.2(.10) + 2.8(.05)] = 8 ( 1 - 0.12 + 0.14) = 8 x 1.02 = 8.16 Demand for automobiles : Q2 = 8.16 million cars. Q10.Illustration: Cross elasticity as a measure of the effect of change in the fares on the demand for rail service and vice-versa. The cross elasticity of demand for a train service from station A to station B is the rate of change in the number of train tickets sold on that route in relation to the percentage change in the price of Bus service for the same route. If the bus company reduced its fare from Rs.40 to 35, the following data is observed: __________________________________________________________________ ______ Fare (Rs.) Daily No. of Pasengers Bus Rail Bus Rail Before fare change 45 40 500 200 After fare change 45 35 400 300 6
• 7. Percentage change 0 -12.5% -20% 50% Cross elasticity ec = %Q in Rail service = -20% = 1.6 %P in Bus service -12.5% Such a high cross elasticity reflects that the market demand is greatly responsive to the competitive price variation. Advertising or Promotional Elasticity of Demand: Q11.In case several products, the market demand is influenced through advertisement or promotional efforts. The demand function in this case may be stated as : Qx = f (A), Where Qx = demand for the product X measured through the quantity sold in the market.