Consider a competitive market for which the quantities demanded and supplied$($per year$)$ at various prices are given as$$ follows:

Price$($Dollars$)$

Demand$($Millions$)$

Supply$($Millions$)$

$60$

$22$

$14$

$80$

$20$

$16$

$100$

$18$

$18$

$120$

$16$

$20$

$1.$ Derive the inverse demand function and the demand function.

The inverse demand function is

$$

Upper P equals negative one tenth Upper Q plus $62\mathrm{.}2$

$.($Enter your response as an equation in terms of P and Q$.)$

The demand function is

select: Q $=10$P $-622.$

Upper Q equals $10$ Upper P minus $622..($Enter your response as an equation in terms of P and Q$.)$

$2.$ Derive the inverse supply function and the supply function.

The inverse supply function is

$$

Upper P equals $10$ Upper Q minus $80.($Enter your response as an equation in terms of P and Q$.)$

The supply function is

$$

Upper Q equals StartFraction left parenthesis Upper P plus $80$ right parenthesis Over $10$ EndFraction

$.($Enter your response as an equation in terms of P and Q$.)$

$3.$ What are the equilibrium price and$$ quantity?

The equilibrium price is $$$

$$

enter your response here and the equilibrium quantity is

$$

enter your response here million. $($Enter your response as an integer.$)$

$4.$ Suppose the government sets a price ceiling of $$$$60.$

There will be a

$$

of

$$

enter your response here million units. $($Enter your response as an integer.$)$