1. Consider the following demand and supply curves for the automobile industry:
ID: 1093890 • Letter: 1
Question
1. Consider the following demand and supply curves for the automobile industry: QD= 200P^1.2 QS = 1.3P, where P is measured in thousands of dollars and Q in millions of automobiles. (a) Find the equilibrium price and quantity. (b) Suppose now that government policy restricts automobile sales to 11 (million) in order to control emissions of pollutants. An approximation to the direct welfare loss from such a policy is $2.4 billion. How does the size of the total welfare loss from a quantity restriction depend on the elasticities of supply and demand? What determines how the loss will be shared?Explanation / Answer
a. At equilibrium: Qd = Qs
=> 200P^-1.2 = 1.3P
=> 200 = 1.3P^2.2
=> P = (200/1.3)^(1/2.2) = 9.86575 => P = $9865.75
Q = 1.3P = 1.3*9.86575 = 12.825 million vehicles.
b. The relative elasticities of demand and supply determine who suffers the more welfare loss.
If the demand elasticity is higher than supply elasticity, the producers bear more of the welfare loss.
If the demand elasticity is lower than supply elasticity, the consumers bear more of the welfare loss.
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