PS#1 (ans).docx - Solution for Problem Set#1 1(18pts Market...

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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 Q d = 500,000 – 4P + 2P Maserati + 25,000P gas , where P is the price of big SUVs (in thousands of dollars), P Maserati is the price of a Maserati Ghibli, and P gas is the price for a gallon of gasoline. Assume that supply is given by Q s = -10,000 + 5P - 0.2P Battery . P is the price of a lithium battery for the Tesla Model S. Assume: P Maserati = $100,000; P gas = $4/gallon; and P Battery =$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 + 2P Maserati + 25,000P Gas P Maserati = $100,000, P gas = $4 Q d = 500,000 - 4P + 2(100,000) + 25000(4) Q d = 800,000 – 4P Q s = -10,000 + 5P - 0.2P Battery P Battery =$20,000 Q s = -10,000 + 5P - 0.2(20,000) Q s = -14,000 + 5P Inverse Demand Curve P = 200,000 – (1/4) Q d Inverse Supply Curve P = 2,800+(1/5)Q s 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
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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 * P wr /Q x = 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
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Q*= 428,222 d) (2pts) Ceteris paribus, what is the market equilibrium P* and Q* when the price of lithium batteries increases by $10,000. Q d = 800,000 – 4P Q s = -10,000 + 5P - 0.2(42,500) Q s = -10,000 + 5P – 8,500 At equilibrium, S = D 800,000 – 4P=-18,500 + 5P 818,500=9P $90,944=P* 436,222=Q* e) (4pts) Now suppose the government wants to impose a tax on Tesla’s because it wants to tax the rich and believes that people who buy Teslas tend to be wealthy. The government sets the tax equal to $10,000 per car. Model the tax placed on consumers as a shift in the demand curve. Show the change in your graph and the new equilibrium P* and Q*. (Fully label) Does it matter if the tax is placed on consumers rather than the producer of Tesla? Prove your answer by algebra and in a graph.
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