1. the demand curve Q = 2000 – 2 P,for product X is given as
Given Q = 2000 – 2 P, therefore therefore P = 1000 – Q/2 a) how many units will be sold at $10?
Q = 2000 – 2 P Therefore, Q = 2000 - 2 (10) (10) = 1980 b) write equations for total revenue and marginal revenue ( in terms of P)
TR = P *Q = P (2000 – 2P) = 2000 P – 2 P2 ( in terms of P) TR = P *Q = Q (1000 – Q/2) = 1000 Q – Q2/2 This is important as we can find Marginal revenue only from TR (in terms of Q)
MR = δTR /δQ (one unit change in TR because ofa unit change in Q) Therefore MR = 1000 – Q MR = 1000 – Q = 1000 – (2000 – 2P) = 2P – 1000 (in terms of P) c) what will be the total revenue at a price of $70? What will be the marginal revenue?
TR = 2000 P – 2 P2, substitute for P =70 TR = 130200 MR = 2P – 1000, substitute for P =70 MR = -860 d) what is the point elasticity at a price of $70?
Ep = (δQ /δP)* (P/Q) You get (δQ /δP) = -2 by differentiating Q = 2000 – 2 P, substitute the value of Q when P = 70 Therefore Ep = -2 * (70 / 1980) = -0.0753 e) at what price would elasticity be unitary?
Ep = 1, therefore │1│= │ -2 * P/(2000 – 2P)│ ½ = P/ (2000-2P), therefore P = 500
f) calculate arc elasticity at the interval between $60 and $70.
Ep = (Q2 – Q1)/(P2-P1) * (Q2 + Q1)/(P2 + P1) We get for P = 60, Q = 1880 and for P = 70, Q = 1860 Therefore Ep = (1880- 1860)/(60-70) * (1880 + 1860)/(60 + 70) = - 0.0695
2. The ABC company manufactures AM/FM clock radios and sells on average 3000 units monthly at $25 each to retail stores. Its closest competitor produces a similar type of radio that sells for $28. a) if the demand for ABC’s product has an elasticity coefficient of -3, how much will it sell
per month if the price is lowered to $22.
Ep = (Q2 – Q1)/(P2-P1) * (Q2 + Q1)/(P2 + P1) Where Ep = -3, Q2 = ?, Q1 = 3000, P2 = 22, P1 = 25, substituting in the arc elasticity formula above, Q2 = 4421.05 approx 4421 b) the competitor decreases its prices to $24. It cross-elasticity between the two radios is 0.3, what will be the ABC’s monthly sales be?
Cross elasticity Ep = (Qx2 – Qx1)/(Py2-Py1) * (Qx2 + Qx1)/(Py2 + Py1) Assuming Qx1 = 3000, Qx2 = ?, Py2 = 24, Py1 = 28 Substituting, Qx2 = 2864.66 approx 2864 Assuming Qx1 = 4421, Qx2 =?, Py2 = 24, Py1 = 28 Substituting, Qx2 = 4221 3) In the electronic market of Nehru Place, the demand function as analysed by Pankaj Electronics for its LCD TV sets is P = 12000 – 6Q. find out, a) the marginal revenue function for the same,
TR = P *Q = 12000 Q – 6 Q2 MR = δTR /δQ = 12000 – 12 Q = 1000 – Q
b) at what price and quantity will marginal revenue be zero
putting MR = 0, Q = 1000, P = 6000 4) In the electronic market of Nehru Place, the demand function as analysed by Pankaj Electronics for its LCD TV sets is P = 12000 – 6Q. find out, a) what is the point elasticity at a price of $70,
Ep = (δQ /δP)* (P/Q) Differentiate Q = 2000 – (1/6) P, (δQ /δP = -1/6 For P = 70, Q = 1988 Ep = -1/6*(70/1988) = -0.0058 b) at what price would elasticity be unitary? Ep = 1, therefore │1│= │-1/6 * P/(2000 – P/6)│ 6(2000 – P/6) = P P = 6000
