IAS 106 - Problem set #1 . Questions and Answers

IAS 106 - Problem set #1 . Questions and Answers Solution for Problem Set #1 1. (18pts) Market Demand and Elasticities: Consider the demand for a Tesla Model S. Suppose that the demand for a Tesla Model S is Qd = 500,000 – 4P + 2PMaserati + 25,000Pgas, where P is the price of big SUVs (in thousands of dollars), PMaserati is the price of a Maserati Ghibli, and Pgas is the price for a gallon of gasoline. Assume that supply is given by Qs = -10,000 + 5P - 0.2PBattery. P is the price of a lithium battery for the Tesla Model S. Assume: PMaserati = $100,000; Pgas = $4/gallon; and PBattery=$20,000. a) (3pts)What is the equilibrium price and quantity for a Tesla Model S? Graph your supply and demand equations in inverse form (i.e. price on left side of equation and Q on the right) and show the equilibrium P*, Q*. Q d = 500,000 - 4P + 2PMaserati + 25,000PGas PMaserati = $100,000, Pgas = $4 Q d = 500,000 - 4P + 2(100,000) + 25000(4) Q d = 800,000 – 4P Q s = -10,000 + 5P - 0.2PBattery PBattery=$20,000 Q s = -10,000 + 5P - 0.2(20,000) Q s = -14,000 + 5P Inverse Demand Curve  P = 200,000 – (1/4) Qd Inverse Supply Curve  P = 2,800+(1/5)Qs At equilibrium, S = D  -14,000+5P= 800,000 – 4P 9P=814,000 P*=$90,444 • Q* = -10,000+5(90,444) or Q*=800,000-4(90,444) Q* = 438,222 a (2pts) At market equilibrium, what are the coefficients for the price elasticity of demand and supply for the Tesla Model S? = Q d /P * P/Q = -4 * (90,444/438,222) = -0.825 Q/P * P/Q = 5 * (90,444/438,222) = 1.031 b) (2pts) What is the cross-price elasticity of demand for the Tesla Model S with gasoline? How would you describe the relationship between the Tesla and gas? Cross Price = Q x /P wr * Pwr/Qx = 25,000 * (4/438,222) = 0.228 As you are probably already aware, Tesla makes cars that run on electricity charged batteries, therefore it is a substitute to gasoline powered cars. Mathematically, from the positive cross-price elasticity coefficient, we can conclude that a Tesla Model S is a substitute to gasoline. When the price of gas increases demand for Tesla increases. c) (2pts) Ceteris paribus, what is the market equilibrium P* and Q* when the price of a Maserati Ghibli falls by $9,000? Q d = 500,000 - 4P + 2(91,000) + 25000(4) Q d = 782,000 – 4P Q s = -14,000 + 5P S=D 9P= 796,000 P*= $88,444