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- Assume that we have a Cobb-Douglas type aggregate production function in the form:
Y=KaLb
a-)Briefly explain why y''≤0
b-) Find the elasticity of substitution between K and L. What does expansion path look like?
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Solved in 2 steps
- Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = Ka.Lb c. Briefly explain why y'>0 or dy/dk > 0 . Is it possible that dy/dk < 0 ? Why? d. Briefly explain why y'' ≤ 0 . e. Find the elasticity of substitution between K and L. What does expansion path look like?Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from previous question (Question-1) (Y=Ka.Lb) ? (Question 1: Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=Ka.Lb )Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from previous question (Question-1) (Y=Ka.Lb) ?
- Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=Ka.Lba. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or y- or dy/dk ? c. Briefly explain why y’>0 or =dy/dk >0 . Is it possible that dy/dk>0 ? Why? d. Briefly explain y’’ < 0 e. Find the elasticity of substitution between K and L. What does expansion path look like?Consider an economy in which the aggregate production function is given by the equation: Y = 3.6 K0.5 N0.5 where (Y) is aggregate production, (A) measures productivity, (K) is the stock of physical capital and (N) is the amount of labor, measured in millions of workers. Both Y and K are measured in billions of reais. K is given and is 10,000 (i.e., 10,000 billion reais), so K0.5 = 100. The aggregate labor supply is given by the following equation: NS = [(1-t).w]2 where (t) is the income tax rate on labor and (w) is the real wage, measured in reais per hour. t = 0.20 (20%). The equilibrium levels of the real wage (w) and employment (N) are, respectively, [ANSWER] and [ANSWER]. The full employment production level (Y) is [ANSWER]. Finally, the after-tax real wage that workers receive per hour in this economy iConsider a competitive, closed economy with a Cobb-Douglas production function with parameter α = 0.25. The parameter A is equal to 60. Assume also that capital is 100, labor is 100. Calculate GDP (Y) for this economy. Does the production function exhibit constant returns to scale? Demonstrate with examples. Determine if the production function exhibits diminishing marginal returns to capital. Demonstrate with calculus What is the real wage in this economy? What share of GDP will go to labor in this economy?
- Consider a Cobb-Douglas production function, Y=zKα(Nd)1−α, with 0< α <1. (a) Show that this production function exhibits constant returns to scale. (That is, show that when K becomes xK and Nd becomes xNd, Y becomes xY for x > 0. (b) What is MPN? Is it increasing or decreasing in Nd?Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = Ka.Lb a. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or or y' or dy/dk ? c. Briefly explain why y'>0 or dy/dk > 0 . Is it possible that dy/dk < 0 ? Why? d. Briefly explain why y'' ≤ 0 . e. Find the elasticity of substitution between K and L. What does expansion path look like?Refer to the figure above. The country of Kemper is on its aggregate production function at point W in the above figure. If the population increases with no change in capital or technology, what will happen to the economy? Explain your answer.
- Consider a total of N = 62 identical firms such that firm i produces qi units of output using Li units of labour according to the production function qi = 11 Li 1/2 + Li , i = 1, ..., N. Use the method of Lagrange to derive the aggregate production function given there is a total of L units of labour to be allocated among firms. Then find and enter below the value of the Lagrangian multiplier at the optimal point assuming L = 1854. Please do fast ASAP fastWhich is an example of the aggregate production function, Y = F(K, N), that exhibits constant returns to scale? Y= 2 K N Y = 3 K N Y = K/N Y= 2K + 3 N) What is the equation of the long-run aggregate supply curve? The income velocity of money is constant, and the money supply is fixed: V = 0.15 M = 5600 The production function is Y = F(L, K) = 8 x √L x √K The endowment of resources is given by the input combination (L, K) = (49, 25)
