Two functions, u(x,y) and v(x,y), are said to verify the
Cauchy-Riemann
differentiation equations if they satisfy...
Two functions, u(x,y) and v(x,y), are said to verify the
Cauchy-Riemann
differentiation equations if they satisfy the following
equations ∂u\dx=∂v/dy and ∂u/dy=−(∂v/dx)
a. Verify that the Cauchy-Riemann differentiation equations can
be written in the polar coordinate form as
∂u/dr=1/dr ∂v/dθ and ∂v/dr =−1/r ∂u/∂θ
b. Show that the following functions satisfy the Cauchy-Riemann
differen- tiation equations
u=ln sqrt(x^(2)+y^(2)) and v= arctan y/x.
Suppose your utility function is given by U(x,y)=xy2 . The price
of x is Px, the...
Suppose your utility function is given by U(x,y)=xy2 . The price
of x is Px, the price of y is Px2 , and your income is
M=9Px−2Px2.
a) Write out the budget constraint and solve for the MRS.
b) Derive the individual demand for good x. (Hint: you need to
use the optimality condition)
c) Is x an ordinary good? Why or why not?
d) Suppose there are 15 consumers in the market for x. They all
have individual demand...
Verify the Caucy-riemann equations for the functions u(x,y),
v(x,y) defined in the given domain
u(x,y)=x³-3xy², v(x,y)=3x²y-y³,...
Verify the Caucy-riemann equations for the functions u(x,y),
v(x,y) defined in the given domain
u(x,y)=x³-3xy², v(x,y)=3x²y-y³, (x,y)ɛR
u(x,y)=sinxcosy,v(x,y)=cosxsiny (x,y)ɛR
u(x,y)=x/(x²+y²), v(x,y)=-y/(x²+y²),(x²+y²), (
x²+y²)≠0
u(x,y)=1/2 log(x²+y²), v(x,y)=sin¯¹(y/√¯x²+y²), ( x˃0 )
In each case,state a complex functions whose real and imaginary
parts are u(x,y) and v(x,y)
Suppose f is entire, with real and imaginary parts u and v
satisfying u(x, y) v(x,...
Suppose f is entire, with real and imaginary parts u and v
satisfying u(x, y) v(x, y) = 3 for
all z = x + iy. Show that f is constant.
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2. Consider a consumer with preferences represented by the
utility function:
u(x,y)=3x+6sqrt(y)
(a) Are these preferences...
2. Consider a consumer with preferences represented by the
utility function:
u(x,y)=3x+6sqrt(y)
(a) Are these preferences strictly convex?
(b) Derive the marginal rate of substitution.
(c) Suppose instead, the utility
function is:
u(x,y)=x+2sqrt(y)
Are these preferences strictly convex?
Derive the marginal rate of sbustitution.
(d) Are there any similarities or differences between the two
utility functions?
Consider a consumer with preferences represented by the utility
function
u(x,y)=3x+6 sqrt(y)
(a) Are these preferences...
Consider a consumer with preferences represented by the utility
function
u(x,y)=3x+6 sqrt(y)
(a) Are these preferences strictly convex?
(b) Derive the marginal rate of substitution.
(c) Suppose instead, the utility function is:
u(x,y)=x+2 sqrt(y)
Are these preferences strictly convex? Derive the marginal rate
of substitution.
(d) Are there any similarities or differences between the two
utility functions?
If z=(x+4y)ex+y,x=ln(u),y=v,z=(x+4y)ex+y,x=ln(u),y=v, find
∂z∂u∂z∂u and ∂z∂v∂z∂v. The variables are restricted to domains on
which the functions...
If z=(x+4y)ex+y,x=ln(u),y=v,z=(x+4y)ex+y,x=ln(u),y=v, find
∂z∂u∂z∂u and ∂z∂v∂z∂v. The variables are restricted to domains on
which the functions are defined.
if y=uv, where u and v are functions of x, show that the nth
derivative of...
if y=uv, where u and v are functions of x, show that the nth
derivative of y with respect to x is given by
(also known as Leibniz Rule)
A consumer has preferences represented by the utility function
u(x, y) = x^(1/2)*y^(1/2). (This means that...
A consumer has preferences represented by the utility function
u(x, y) = x^(1/2)*y^(1/2). (This means that
MUx=(1/2)x^(−1/2)*y^(1/2) and MUy =1/2x^(1/2)*y^(−1/2)
a. What is the marginal rate of substitution?
b. Suppose that the price of good x is 2, and the price of good
y is 1. The consumer’s income is 20. What is the optimal quantity
of x and y the consumer will choose?
c. Suppose the price of good x decreases to 1. The price of good
y and...
Suppose a consumer's preferences are given by U(X,Y) = X*Y.
Therefore the MUX = Y and...
Suppose a consumer's preferences are given by U(X,Y) = X*Y.
Therefore the MUX = Y and MUY = X. Suppose
the price of good Y is $1 and the consumer has $80 to spend (M =
80). Sketch the price-consumption curve for the
values
PX = $1
PX = $2
PX = $4
To do this, carefully draw the budget constraints associated with
each of the prices for good X, and indicate the bundle that the
consumer chooses in each...