Question

Assume that the quantity demanded (Q) for a certain good is Q = 1000 − 20p, where p is the price in dollars. Assume that 0 ≤ p ≤ 50.

(A) Graph the demand curve. Put p on the horizontal (x) axis.

(B) Is the demand a monotonic function of p? Is it continuous? Smooth?

(C) Find the inverse demand function by solving for p in terms of Q.

(D) Graph the demand curve. This time, put p on the vertical (y) axis.

(E) Assume that the supply function is S(p) = p 2 + p. Graph the supply function. Find the equilibrium price p ∗ and quantity Q∗ = S(p ∗ ).

(F) Starting from equilibrium, assume that the price increases 1%. What is the corresponding percent increase in quantity supplied? What is the percent decrease in quantity demanded?

Answer 1

B.yes the demand function of p is a monotonic transformation.If the demand function is multiplied by 2 then also the slope remains the same.Therefore,the demand function is a monotonic transformation.

E.

At equilibrium Quantity demanded=Quantity supplied

1000-20p=p^2+p

p^2+21p-1000=0

P=22 approx.

S(p)=(22)^2+22

S(p)=506

F.1% of 22=.22

Final price=22.22

At this price quantity supplied=515.9484

%Change=(Qs final-Qs initial/Qs initial)*100=1.96%