Consider two countries Frugalia and Prodigalia (we can call F and P). In both co
ID: 1196270 • Letter: C
Question
Consider two countries Frugalia and Prodigalia (we can call F and P). In both countries the production function is Cobb-Douglas: Y=A*(K^0.5)*(N^0.5). The population growth rate is 0.2, physical capital depreciates at the rate of 0.3, and A = 10. In F, the savings rate Sf = 0.6 and in P it is Sp = 0.4.
a. write the production function in terms of output per capita
b.find the stready-state values of capital-labor ratio(K/N) in both counties.
c. find the steady-state values of output per capita(Y/N) in both counties.
d. in which counties is the marginal product of labor higher in the steady state?
e.in which of the counties is counsumption percapita higher in the steady state?
Explanation / Answer
Y = A. K0.5N0.5
(a) Dividing both sides by N,
(Y / N) = A. (K / N)0.5
y = A. k0.5
y = 10. k0.5 [Since A = 10]
This is the production function of output per capita in terms of capital per capita.
(b) If s: Savings rate, d: Depreciation rate, n: Population growth rate,
s / (d + n) = k / y
s / (0.3 + 0.2) = k / (10. k0.5)
s / 0.5 = k0.5 / 10
s x 20 = k0.5
(1) Country F:
0.6 x 20 = k0.5
k = (12)2 = 144
(2) Country P
0.4 x 20 = k0.5
k = (8)2 = 64
(c) y = 10. k0.5
(1) Country F
y = 10 x 12 = 120
(2) Country P
y = 10 x 8 = 80
(d) Marginal product of labor, MPL = dY / dN
Since Y is the same in both countries, MPL will be the same in both countries.
(e) Consumption per capita, c = y - sy
(1) Country F
c = 120 - (0.6 x 120) = 120 - 72 = 48
(2) Country P:
c = 80 - (0.4 x 80) = 80 - 32 = 48