Question

Microeconomics...

2. For the car industry of nation \(\mathrm{A}\), the market demand is

$$ Q_{D}(P, I)=2000 \times P^{-2} I^{0.5} $$

where \(I\) is income.

a. Compute the price elasticity \(e_{D, P}\) and income elasticity \(e_{D, I}\) of the car demand

b. Suppose there is a \(10 \%\) increase of income \(I\). We do not know the supply function \(Q_{S}(P)\), but knows that the supply elasticity is \(e_{S, P}=3\) from empirical data. Predict how much the equilibrium price will increase (in percentage).

Answer 1

(a) Price elasticity of demand

Q=2000

$q=2000P^{^{-2}}I^{0.5} \partial Q/\partial p=2000(-2)P^{-3}I^{^{^{0.5}}}$

=1/2

$q=2000P^{^{-2}}I^{0.5} \partial Q/\partial p=2000(-2)P^{-3}I^{^{^{0.5}}} = -4000p^{^{-3}}I^{0.5} \eta d=\partial q/\partial pXp/q$$q=2000P^{^{-2}}I^{0.5} \partial Q/\partial p=2000(-2)P^{-3}I^{^{^{0.5}}} = -4000p^{^{-3}}I^{0.5} \eta d=\partial q/\partial pXp/q =4000P^{-3}I^{0.5XP}/2000P^{-2}I^{0.5} =4000P^{-2}I^{0.5}/2000P^{-2}I^{_{0.5}} =2$$q=2000P^{^{-2}}I^{0.5} \partial Q/\partial p=2000(-2)P^{-3}I^{^{^{0.5}}} = -4000p^{^{-3}}I^{0.5} \eta d=\partial q/\partial pXp/q =4000P^{-3}I^{0.5XP}/2000P^{-2}I^{0.5} =4000P^{-2}I^{0.5}/2000P^{-2}I^{_{0.5}}$$q=2000P^{^{-2}}I^{0.5} \partial Q/\partial p=2000(-2)P^{-3}I^{^{^{0.5}}} = -4000p^{^{-3}}I^{0.5} \eta d=\partial q/\partial pXp/q =4000P^{-3}I^{0.5XP}/2000P^{-2}I^{0.5} =4000P^{-2}I^{0.5}/2000P^{-2}I^{_{0.5}}$$q=2000P^{^{-2}}I^{0.5} \partial Q/\partial p=2000(-2)P^{-3}I^{^{^{0.5}}} = -4000p^{^{-3}}I^{0.5} \eta d=\partial q/\partial pXp/q =4000P^{-3}I^{0.5XP}/2000P^{-2}I^{0.5} =4000P^{-2}I^{0.5}/2000P^{-2}I^{_{0.5}}$$q=2000P^{^{-2}}I^{0.5} \partial Q/\partial p=2000(-2)P^{-3}I^{^{^{0.5}}} = -4000p^{^{-3}}I^{0.5} \eta d=\partial q/\partial pXp/q =4000P^{-3}I^{0.5XP}/2000P^{-2}I^{0.5} =4000P^{-2}I^{0.5}/2000P^{-2}I^{_{0.5}}$$q=2000P^{^{-2}}I^{0.5} \partial Q/\partial p=2000(-2)P^{-3}I^{^{^{0.5}}} = -4000p^{^{-3}}I^{0.5} \eta d=\partial q/\partial pXp/q =4000P^{-3}I^{0.5XP}/2000P^{-2}I^{0.5} =4000P^{-2}I^{0.5}/2000P^{-2}I^{_{0.5}}$$q=2000P^{^{-2}}I^{0.5} \partial Q/\partial p=2000(-2)P^{-3}I^{^{^{0.5}}} = -4000p^{^{-3}}I^{0.5} \eta d=\partial q/\partial pXp/q =4000P^{-3}I^{0.5XP}/2000P^{-2}I^{0.5} =4000P^{-2}I^{0.5}/2000P^{-2}I^{_{0.5}}$$q=2000P^{^{-2}}I^{0.5} \partial Q/\partial p=2000(-2)P^{-3}I^{^{^{0.5}}} = -4000p^{^{-3}}I^{0.5} \eta d=\partial q/\partial pXp/q =4000P^{-3}I^{0.5XP}/2000P^{-2}I^{0.5} =4000P^{-2}I^{0.5}/2000P^{-2}I^{_{0.5}} \eta d=2$Income elasticity of Car

$d=2000P^{-2}I^{0.5}$

=

$=1000P^{-2}I^{^{-0.5}}$

$\eta I=\partial Q/\partial IXI/Q$$\partial q/\partial I=2000P^{-2}(0.5)I^{0.5}$