Assume the following production function: Y=8K^(0.3)N^(0.7) a) Keeping capital constant, show graphically a technological improvement. (10...
Assume the following production function: Y=8K^(0.3)N^(0.7)
a) Keeping capital constant, show graphically a technological improvement. (10 marks)
b) If the capital stock is K = 30, and the prevailing wage rate is w* = $25, find the full employment. (10 marks)
Homework Answers
We have a production function: Y = 8K^(0.3)N^(0.7) where technology parameter is 8.
a) Keeping capital constant, If there is a technological improvement, it will increase the overall productivity of both labor and capital. Now that capital is fixed, and only labor is variable, with increase in labor units, the new production function will lie above the original one, assuming that technology parameter is increased to 12 and production function is Y = 12K^(0.3)N^(0.7)
b) If the capital stock is K = 30, production function Y = 8*(30^(0.3)*(N^(0.7) = 22.1935(N^(0.7) and the prevailing wage rate is w* = $25, find the MPN
MPN = dY/dN = 0.7*22.1935/N^0.3
At the optimal allocation, MPN = wage rate
25 = 15.5345/N^0.3 and N = 0.204.
This is the optimum amount of labor
Add Answer to:
Assume the following production function: Y=8K^(0.3)N^(0.7)
a) Keeping capital constant, show graphically a technological
improvement. (10...
Assume the following production function: Y=8K^0.3N^0.7 a) Keeping capital constant, show graphically a technological improvement. b)...
Assume the following production function: Y=8K^0.3N^0.7 a) Keeping capital constant, show graphically a technological improvement. b) If the capital stock is K = 30, and the prevailing wage rate is w* = $25, find the full employment.
Assume the following production function: Y=8K^0.3N^0.7 If the capital stock is K = 30, and the...
Assume the following production function: Y=8K^0.3N^0.7 If the capital stock is K = 30, and the prevailing wage rate is w* = $25, find the full employment. （can you please anwering with the detailed calculation steps? Thanks!)
a）Assume that country A has the following production function Y=K^0.3 L^0.7 Its saving rate is 20%...
a）Assume that country A has the following production function Y=K^0.3 L^0.7 Its saving rate is 20% per year. The depreciation rate is assumed to be 5% per year. What is the steady state level of capital stock per capital, K*？What is the steady state level of output per capital, Y*? What is the steady state level of c*? Show the results in a suitable diagram. b) At year 1,K=6. Is this a steady state? Find out the values of GDP...
8. Consider the following production function Y = AK0.3(NH)0.7 where Y is GDP, A is total...
8. Consider the following production function Y = AK0.3(NH)0.7 where Y is GDP, A is total factor productivity, K is capital, N is employment and H is human capital. Denote by P the population of the country. Thus, Y/P is per-capita GDP and N/P is the fraction of the population employed. What is the contribution of the fraction of the population employed (N/P) to the growth rate of per-capita GDP (Y/P)? (a) Growth rate of N/P. (b) Growth rate of...
1) Assume that a country's production function is Y = AK 0.3 L 0.7 (and MPK...
1) Assume that a country's production function is Y = AK 0.3 L 0.7 (and MPK = 0.3 Y/K ) The ratio of capital to output is 3, the growth rate of output is 3 percent, and the depreciation rate is 4 percent. Assume the economy is in a steady state. a.Write down the steady state condition and calculate the saving rate for this steady state. b.Write down the Golden Rule for this economy. Is this economy in the Golden...
8. Suppose that the production function is Y=5K0.5N0.5. With the production function, the marginal product of...
8. Suppose that the production function is Y=5K0.5N0.5. With the production function, the marginal product of labor is MPN=0.5K0.5N-0.5. The capital stock is K=30. The labor supply curve is NS=100[(1-t)w]2, where w is the real wage rate, t is the tax rate on labor income, and hence (1-t)w is the after-tax real wage rate. a) Assume that the tax rate on labor income, t, equals zero. Find the equation of the labor demand curve. Calculate the equilibrium levels of the real...
Numerical Example: A firm's optimization problem Given: production function: y-10 / KN capital stock K -9,...
Numerical Example: A firm's optimization problem Given: production function: y-10 / KN capital stock K -9, wage w 7.5 Follow these steps: write down the expression for the firm's profit π o optimize: find the profit-maximizing level of employment find output y and profit π
HOMEWORK # 3 Productivity. Outeut and Employment #1 suppose the economy's production function is v-AK0.3 0.7...
HOMEWORK # 3 Productivity. Outeut and Employment #1 suppose the economy's production function is v-AK0.3 0.7 When K 2,000 N=50 what is r? (in % form and 1 decimal) #2 According to Okun's law, if actual output grew 3% and full-employment output rose 5%, what would be the change in the unemployment rate? #3 Cupcake Stand # Cupcakes Produced # workers 0 12 30 36 40 If Cupcakes sell for $5 each and the wage rate (nominal) is $40, how...
Question 2 130 marks] Suppose that the production function is given by Y 0.5VKv/N. Assume that...
Question 2 130 marks] Suppose that the production function is given by Y 0.5VKv/N. Assume that the size of the population, the labour participation rate and the unemployment rate are all constant. a) Does this production function exhibit constant returns to scale? Explain (5 marks) b) Explain the difference between returns to factors of production and returns to scale (4 marks) cTransform the production function into a relationship between output per worker and capital per worker. (5 marks) d) Assume...
d. Assume that the aggregate production function is given by: where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume...
d. Assume that the aggregate production function is given by: where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume that capital depreciates at a rate of δ, the rate of technological progress is g, the population is growing at a rate of n and the saving rate is s. I5 marks] i. Determine the scale of production? Suppose capital is increased by a...
8. Consider the following production function Y = AK0.3(NH)0.7 where Y is GDP, A is total factor productivity, K is capital, N is employment and H is human capital. Denote by P the population of the country. Thus, Y/P is per-capita GDP and N/P is the fraction of the population employed. What is the contribution of the fraction of the population employed (N/P) to the growth rate of per-capita GDP (Y/P)? (a) Growth rate of N/P. (b) Growth rate of...
Numerical Example: A firm's optimization problem Given: production function: y-10 / KN capital stock K -9, wage w 7.5 Follow these steps: write down the expression for the firm's profit π o optimize: find the profit-maximizing level of employment find output y and profit π
HOMEWORK # 3 Productivity. Outeut and Employment #1 suppose the economy's production function is v-AK0.3 0.7 When K 2,000 N=50 what is r? (in % form and 1 decimal) #2 According to Okun's law, if actual output grew 3% and full-employment output rose 5%, what would be the change in the unemployment rate? #3 Cupcake Stand # Cupcakes Produced # workers 0 12 30 36 40 If Cupcakes sell for $5 each and the wage rate (nominal) is $40, how...
Question 2 130 marks] Suppose that the production function is given by Y 0.5VKv/N. Assume that the size of the population, the labour participation rate and the unemployment rate are all constant. a) Does this production function exhibit constant returns to scale? Explain (5 marks) b) Explain the difference between returns to factors of production and returns to scale (4 marks) cTransform the production function into a relationship between output per worker and capital per worker. (5 marks) d) Assume...
d. Assume that the aggregate production function is given by: where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume that capital depreciates at a rate of δ, the rate of technological progress is g, the population is growing at a rate of n and the saving rate is s. I5 marks] i. Determine the scale of production? Suppose capital is increased by a...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago