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.
Homework Answers
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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^(0.3)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)
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!)
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...
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...
Suppose that the production function is Y = 9 60.500.5 With this production function, the marginal...
Suppose that the production function is Y = 9 60.500.5 With this production function, the marginal product of labor is MPN = 4.5 K.5/10.5 The labor supply curve is NS = 105 x[(1 – t)xw], where w is the real wage rate, t is the tax rate on labor income, and hence (1 – t) xw is the after-tax real wage rate. The capital stock is K = 25. Assume that the tax rate on labor income, t, equals zero...
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...
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
Question 3: Productivity, Output, and Employment (20 marks) Assume that the aggregate production is given by...
Question 3: Productivity, Output, and Employment (20 marks) Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. a and B are parameters whose values are between O and I a) Derive an analytical expression for the marginal product of capital (MPK),...
Aamir's company has the production function Q=8K^0.75L^0.25, where Q measures output, K measures machine hours, and...
Aamir's company has the production function Q=8K^0.75L^0.25, where Q measures output, K measures machine hours, and L measures labor hours. Suppose that the rental rate of capital is R=$120, the wage rate is W=$20, and the firm wants to produce 800 units of output. Use the Lagrange method to find the optimal input mix. What the optimal level of K?
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...
Suppose that the production function is Y = 9 60.500.5 With this production function, the marginal product of labor is MPN = 4.5 K.5/10.5 The labor supply curve is NS = 105 x[(1 – t)xw], where w is the real wage rate, t is the tax rate on labor income, and hence (1 – t) xw is the after-tax real wage rate. The capital stock is K = 25. Assume that the tax rate on labor income, t, equals zero...
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...
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
Question 3: Productivity, Output, and Employment (20 marks) Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. a and B are parameters whose values are between O and I a) Derive an analytical expression for the marginal product of capital (MPK),...
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...
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