Assume that a certain company's productivity is modelled by the Cobb-Douglas production function f(x, y) = 5xiy3, where x is the amount of money expended for labour and y is the cost of capital equipment. Assume that the company currently spends 20 units on capital equipment. (a) Find all æ such that marginal productivity of labour equals the marginal productivity of capital. (b) Find all æ such that marginal productivity of labour is strictly less than the marginal productivity of capital. (c) Assume the company spends 15 units on labour. To increase productivity, should the company invest in capital expenditures or increase spending on labour? (d) Assume that over time, labour expenditure and capital investments are given by æ(t) = 10 +t, y(t) = 5+t where t denoted time. Compute 4 at t = 0, which is the production rate of change with respect to time at time zero.

Assume that a certain company's productivity is modelled by the Cobb-Douglas production function f(x, y) = 5xiy3, where x is the amount of money expended for labour and y is the cost of capital equipment. Assume that the company currently spends 20 units on capital equipment. (a) Find all æ such that marginal productivity of labour equals the marginal productivity of capital. (b) Find all æ such that marginal productivity of labour is strictly less than the marginal productivity of capital. (c) Assume the company spends 15 units on labour. To increase productivity, should the company invest in capital expenditures or increase spending on labour? (d) Assume that over time, labour expenditure and capital investments are given by æ(t) = 10 +t, y(t) = 5+t where t denoted time. Compute 4 at t = 0, which is the production rate of change with respect to time at time zero.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Assume that a certain company's productivity is modelled by the Cobb-Douglas production function f(x, y) = 5xš y3,
where x is the amount of money expended for labour and y is the cost of capital equipment. Assume that the company
currently spends 20 units on capital equipment.
(a) Find all x such that marginal productivity of labour equals the marginal productivity of capital.
(b) Find all x such that marginal productivity of labour is strictly less than the marginal productivity of capital.
(c) Assume the company spends 15 units on labour. To increase productivity, should the company invest in capital expenditures or increase spending on labour?
(d) Assume that over time, labour expenditure and capital investments are given by
x(t) = 10 +t,
y(t) = 5+ t
where t denoted time. Compute at t = 0, which is the production rate of change with respect to time at time zero.

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