中级微观经济学——垄断,学渣渣我中微其中挂了~各种桑心!

中级微观经济学——垄断,学渣渣我中微其中挂了~各种桑心!
1、Monopoly equilibrium for
D(p) = 100/p
and c(y) = y^2
2、Monopoly equilibrium for
D(p) = 10p−3and
c(y)=2y.
Monopoly equilibrium for
D(p) = a –bp and
c(y)= cy.
Monopol y equilibrium for
constant demandelasticity e and c(y)= cy.
3、Tax on monopolist who has constant marginal cost and is facing linear demand function
4、Tax on monopolist who
has constant marginal cost
and is facing constant
elasticity demand
function.

1.
TR = p*Q = 100
MR = dTR/dQ = 0
MC = dc(Q)/dQ = 2Q
MR = MC
Q = 0
2.
p = 0.1*Q + 0.3
TR = p*Q = 0.1*Q^2 + 0.3*Q
MR = dTR/dQ = 0.2*Q + 0.3
MC = dc(Q)/dQ = 2
MR = MC
0.2*Q + 0.3 = 2
Q = 8.5
p = a/b - Q/b
TR = p*Q = (a/b)*Q - Q^2/b
MR = dTR/dQ = a/b - 2*Q/b
MC = dc(Q)/dQ = c
MR = MC
a/b - 2*Q/b = c
Q = (a - b*c)/2
3.
Before tax,
MC = c
Q = D(p) = a - b*p
p = a/b - Q/b
With tax t per unit,effective demand function is,
p = a/b - Q/b - t
TR = p*Q = (a/b-t)*Q - Q^2/b
MR = dTR/dQ = a/b - t - 2Q/b
MR = MC
a/b - t - 2Q/b = c
Q = (a - b*t - b*c)/2
p = (a/b - t + c)/2
So in order to achieve a desired price p,tax should be
t = a/b + c - 2p
4.
Becore tax,
MC = c
Q = D(p) = a*p^b
p = (Q/a)^(1/b)
With tax t per unit,effective demand function is
p = (Q/a)^(1/b) - t
TR = Q*p = Q^(1+1/b)/a^(1/b) - Q*t
MR = dTR/dQ = (1+1/b)*(Q/a)^(1/b) - t
MR = MC
(1+1/b)*(Q/a)^(1/b) - t = c
Q = a*[(c+t)/(1+1/b)]^b
p = (c+t)/(1+1/b) - t = (c+t/b)/(1+1/b)
t = (1+b)*p - b*c
再问： 大神，介个捏？ 是分完全无弹性和完全弹性吗？ Monopol y equilibrium for constant demandelasticity e and c(y)= cy
再答： 不是。完全弹性时demand curve is flat。完全无弹性时demand curve is vertical。 Constant demand elasticity means Q = D(p) = a*p^e p = (Q/a)^(1/e) TR = Q*p = Q^(1+1/e)/a^(1/e) MR = dTR/dQ = (1+1/e)*(Q/a)^(1/e) MC = dc(Q)/dQ = c MR = MC (1+1/e)*(Q/a)^(1/e) = c Q = a*[c/(1+1/e)]^e
再问： why before tax,MC=c？
再答： TC = c(y) = c*y So MC = dTC/dy = c