Question a
I'll use here the first approach suggested by the hint. The production function is.

Y = A*K^(3/10)*L^(7/10)

Taking the derivative with respect to K, we get:

dY/dK = (3/10)*A*K^(-7/10)*L^(7/10)

Now let's multiply and divide by K:

dY/dK = (3/10)*A*K^(-7/10)*L^(7/10)*K/K

= (3/10)*A*K^(3/10)*L^(7/10)/K

But now, notice that A*K^(3/10)*L^(7/10) is equal to Y. Therefore we get:

dY/dK = (3/10)*Y/K

Since we know that K/Y=3 (because capital to output ratio is 3), then Y/K = 1/3, so we get:

dY/dK = 1/10

Question b
In the steady state, the growth of output should equal (n+g). Here's the mathematical proof. I will use the following notation: the derivative of a variable X with respect to time will be simply X'. So when I write Y', I will be talking about dY/dt, ie the derivative of output with respect to time.

In the Solow model with change in technology (as in this question) the steady state is assumed to be reached when the output per "effective labour" is growing at rate zero. Just as Y/L denotes capital-per-labour unit, Y/(A*L) is the capital-per-effective-labor. Intuitively, labour is adjusted by the technology level, hence the term "effective" labour. So we have that, in the ...

Now we will solve for the steady state in a calibration of the US economy in 2000. In
this problem, you will assume that the rate of growth of the work force is n = 0.017 and
there is no exogenous technological progress. The aggregate production function for the
US economy in 2000 is Y = (11.5)K 1/3 L 2/3 . The units are bill

The following question was posed in reference to behavior that deviates from that of the Golden Rule: many of the most bigoted people in the South during the Civil Rights Movement in the 60's were deeply religious people. How do they reconcile this type of behavior with the Golden Rule?

A producer is hiring 20 units of labor and 6 units of capital (bundle A). The price of labor is $10, the price of capital is $2, and at A, the marginal products of labor and capital are both equal to 20. In equilibrium:
a. MPL = MPK
b. MPK will be more than 20
c. MPK will be less than 20
d. MPL will be 5 times MPK
e. None o

Given the following function:
T=aK^-b L^c F^d = 0.02K ^-0.25 L^0.2 F^0.55
if K=100
L = 500
F =20,000
i) Calculate the marginal products associated with K L F.
ii) What is the MRTS between K and L
iii) What is the MRTS between K and F

Consider the following system in Fig.2 (see attached file). Determine the steady state error for unit ramp input. What will be the effect of B and K on steady-state error?

A countries production function is Y=5K^.5 L^.5
Assume that the rate of depreciation as well as the rate of saving are each .10. Also assume that there is no technological nor population growth.
A. What is the steady state level of capital per worker?
B. What is the steady state level of output per worker?
C. Suppose that t

Let the production function be given by
Q = K^1/2*L^1/2, WL=$5, WK=$20,
Suppose the plant size (K) is fixed in the short run at 100.
A. With K = 100, how many units of L are required to produce 400 units of
output?
a. 400
b. 100
c. 1600
d. 3200
e. none of the above
B. If this amou

Just before the switch is opened at t=0, the current through the inductor is 1.70 mA in the direction shown in figure (PLEASE SEE ATTACHMENT). Did steady-state conditions exist just before the switch was opened?
L = 0.9 mH;
R1 = 6k Ohm;
R2 = 6k Ohm;
R3 = 3k Ohm;
Vs = 12V

Solve the following linear, first-order differential equations and ensure that the initial conditions are satisfied. Show whether or not the steady-state solutions are stable.
(a) 10y' = 5y and y(0) = 1. The answer is y(t) = e^(1/2t), but having trouble arriving at that answer
(b) 4y' - 4y = -8 and y(0) = 10. The answer