Question

Q=50-4P 

Q=15+P 

what is the surplus in the market if the government sets a price floor of P=10?  

d) what is the shortage in the market if the government imposes a price ceiling of P=5? 

e) calculate the price elasticities of demand and supply when P=7 

f) calculate the price elasticities of demand and supply when P=10.

Answer 1

Surplus

$Q$ $=$ 50$-$ 4$($10$)$

$Q$ $=$ 50 $-$ 40

$Q$ $=$ 10

$Q$ $=$ 15 $+$ $($10$)$

$Q$ $=$ 15 $+$ 10

$Q$ $=$ 25

Surplus $=$ 25 $-$ 10 $=$ 15

d$)$ Shortage

$Q$ $=$ 50$-$ 4$($5$)$

$Q$ $=$ 50 $-$ 20

$Q$ $=$ 30

$Q$ $=$ 15 $+$ $($ 5)

$Q$ $=$ 15 $+$ 5

$Q$ $=$ 20

Shortage $=$ 20 $-$ 30 $=$ $-$ 10

e$)$ Price elasticities of demand and supply when P=7

$$ Using $($ Arc$)$ or midpoint method of elasticity

Price elasticity of Supply

$Q_o$ $=$ 15 $+$ $($10)

$Q_o$ $=$ 15 $+$ 10

$Q_o$ $=$ 25

$Q_1$ $=$ 15 $+$ $($7)

$Q_1$ $=$ 15 $+$ 7

$Q_1$ $=$ 22

$\%$ Change in quantity $=$ $\frac{Q_1 -Q_o}{(P_1+p_0)/2}$

Price elasticity of supply $=$ $\frac{22-25}{(7+10)/2}$

Price elasticity of supply $=$ $\frac{-3}{8.5}$ $=$ 0.353

Price elasticity or demand

$Q_o$ $=$ 50$-$4 $($10)

$Q_o$ $=$ 50 $-$ 40

$Q_o$ $=$ 10

$Q_1$ $=$ 50 $-$4$($7)

$Q_1$ $=$ 50 $-$ 28

$Q_1$ $=$ 22

$\%$ Change in quantity $=$ $\frac{Q_1 -Q_o}{(P_1+p_0)/2}$

Price elasticity of demand $=$ $\frac{22-10}{(7+10)/2}$

Price elasticity of demand $=$ $\frac{12}{8.5}$ $=$ 1.411

f) Price elasticity of supply

$Q_o$ $=$ 15 $+$ $($5)

$Q_o$ $=$ 15 $+$ 5

$Q_o$ $=$ 20

$Q_1$ $=$ 15 $+$ $($10)

$Q_1$ $=$ 15 $+$ 10

$Q_1$ $=$ 25

$\%$ Change in quantity $=$ $\frac{Q_1 -Q_o}{(P_1+p_0)/2}$

Price elasticity of supply $=$ $\frac{25-20}{(10+5)/2}$

Price elasticity of supply $=$ $\frac{5}{7.5}$ $=$ 0.666

Price elasticity or demand

$Q_o$ $=$ 50$-$4 $($5)

$Q_o$ $=$ 50 $-$ 20

$Q_o$ $=$ 30

$Q_1$ $=$ 50 $-$4$($10)

$Q_1$ $=$ 50 $-$ 40

$Q_1$ $=$ 10

$\%$ Change in quantity $=$ $\frac{Q_1 -Q_o}{(P_1+p_0)/2}$

Price elasticity of demand $=$ $\frac{10-30}{(10+5)/2}$

Price elasticity of demand $=$ $\frac{-20}{7.5}$ $=$ 2.66