the following demand function for a commodity in a town is given as q=2000+15y-5.5p, where y is income. what will be the income elasticity of demand when per capita income is Rs 15000 and price per unit is Rs 150
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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 men’s 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