Suppose you have $100 to invest. You can hold it in cash, you can deposit it in some savings account that pays a nominal interest rate of 0.5%, or you can invest in physical capital. The real rate of return on capital is 1%. The inflation rate is -1%. The three options are risk free. The optimal decision is to: hold some cash and invest the rest in capital invest the $100 in physical capital deposit the $100 in the savings account hold the 100$ in cash
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- AKL The Suppose the production function takes the form F(K, L) = K+L capital share is equal to: 3 L L+K ĀK K+L(c) Consider the aggregate production function Y = K = 100,000, A = 8, and N = 128. K0.2 (AN)0.8 Compute output when100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.
- *0.65 0.35 where x is the amount of labor and y is the amount of capital. The productivity of a country is given by f(x,y) = 100x (a) Compute the marginal productivities of labor and capital when x = 300 and y = 500. (b) Use part (a) to determine the approximate effect on productivity of increasing capital from 500 to 502 units, while keeping labor fixed at 300 units. (c) What would be the approximate effect of decreasing labor from 300 to 298.5 units while keeping capital fixed at 500 units? (a) The marginal productivity of labor is (Do not round until the final answer. Then round to two decimal places as needed.) The marginal productivity of capital is (Do not round until the final answer. Then round to two decimal places as needed.) (b) When capital is increased from 500 to 502 units, the approximate change in productivity is (Do not round until the final answer. Then round to two decimal places as needed.) (c) When labor is decreased from 300 to 298.5 units, the approximate change…Consider the production function: Q = 2K + 3L. The MRTSLK is:Suppose the production function for a product is z = 65x2/5y3/5 where x is the capital expenditures and y is the number of work-hours. (a) Find the marginal productivity of x. (b) Find the marginal productivity of y.
- Suppose the production function for widgets is given by KL – 0.5K2 – 0.1 L2 , where q represents the annual quantity of widgets produced, K represents annual capital input, and L represents annual labor input. (a). Suppose K=5; what is the average productivity of labor (Average product of Labor, MPL) (b). Suppose K=10; at what level of labor input does the total output reach the maximum?Y=$10 trillion, K=$10 trillion, L=100 million workers Cobb-Douglas Production Function What is the production function ؟؟؟Suppose that the production function is given as follows:TPL = 10L + 5L2 + L3Find the total product, Marginal product and average product when L = 5.
- A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is Capital. Where Q is output, L is labor and K is Capital. (a) What sort of returns to scale characterize this production function? (b) Derive the marginal product of labor and capital. (c) What do we mean when we say the production function is linearly homogenous?Assuming a Cobb-Douglas production function with constant returns to scale, then, as L rises with K and A constant, it will be the case that: (a) Both the marginal product of labour and the marginal product of capital will fall(b) The marginal product of labour will fall and the marginal product of capitall will rise(c) Both the marginal product of labour and the marginal product of capital will rise(d) The marginal product of labour will rise and the marginal product of capital will fallFor each of the following production functions, determine whether it exhibits increasing, constant or decreasing returns to scale: a) Q = 2K + L b) Q = 3L + L/K c) Q = Min(2K,L) d) Q = L*K