Sometimes, we are interested in the rate at which the MRTS diminishes. That is, does the slope of the isoquant flatten out quickly or slowly as the capital is replaced with labor? This is measured by the elasticity of substitution σ which is the percent change in the ratio K/L per a percent change in the MRTS: σ = (dK/L /dMRTS) (MRTS/ K/L)

The problem consider the constant elasticity of substitution production function

q = (L^rho + K^rho )^1/rho

Let rho = 1/2 and rho be any arbitrary constant less than one.

Required:
a. Explain what it means if σ is large and what it means if σ is small.
b. Calculate the MRTS of the constant elasticity of substitution production function.
c. Solve for K/L in terms of the MRTS.

Laval produces lamps and home lighting fixtures. its most popular product is a brushed aluminum desk lamp. this lamp is made from components shaped in the fabricating department and assembled in the assembly department. information related to the 22,000 desk lamps produced annually follows.direct materials $280,000direct labor fabricating department (8,000 dlh × $24 per dlh) $192,000assembly department (16,600 dlh × $26 per dlh) $431,600machine hours fabricating department $15,200mhassembly department $20,850mhexpected overhead cost and related data for the two production departments follow.fabricating assemblydirect labor hours 150,000dlh 295,000dlhmachine hours 161,000mh 128,000mhoverhead cost $400,000 430,000required1. determine the plantwide overhead rate for laval using direct labor hours as a base.2. determine the total manufacturing cost per unit for the aluminum desk lamp using the plantwide overhead rate.3. compute departmental overhead rates based on machine hours in the fabricating department and direct labor hours in the assembly department.4. use departmental overhead rates from requirement 3 to determine the total manufacturing cost per unit for the aluminum desk lamps.

Find the zeros of the polynomial 5 x square + 12 x + 7 by factorization method and verify the relation between zeros and coefficient of the polynomials

Which of the following statements is true of the balanced-scorecard? a. it is a more or less a one-dimensional metric of measuring competitive advantages of a firm. b. it is one of the traditional approaches of measuring firm performance. c. its primary focus is to base a firm's strategic goals entirely on external performance dimensions. d. it attempts to provide a holistic perspective on firm performance.