﻿ECO256 A production function exhibits ______________ return to scale if when all inputs are increased by a given proportion K, output increases by the same proportion *Constant* If output increases by a proportion greater than K, there are ______________ returns to scale *Increasing* If the output increases by a proportion smaller or lesser than K, there are ______________ returns to scale *Diminishing* If the production function is homogeneous of degree greater than, equal to or less than 1, returns to scale are increasing, constant or ______________ *Diminishing* A strict cobb-douglas production function in which α+β= 1, exhibits ______________ returns to scale *Constant* A production in which α+β>1, and α+β<1 exhibits ______________ and diminishing respectively returns to scale respectively *Increasing* Given the production function as Q = 6x2 + 3xy + 2y2. The marginal productivity of factors x & y are ______________ and 3x+4y respectively ­­­­­­­ 12x+3y Given the cob-douglas production function as Q = 0.5K2 - 2KL + L2, the marginal productivity of capital and labour respectively are ______________ and 2L - 2K *K-2L* Multiplication of matrices with dimensions (rXc)1 and (rXc)2, requires that the matrices must be ______________ *Conformable* The determinant /A/ of a 2x2 matrix called a ______________ determinant is derived taking the product of the two elements on the principal diagonal and subtracting from it the product of the two elements off the principal diagonal. *Second-order* The element of matrix remaining after the deletion process form a sub-determinant of the matrix is called ______________ *Minor* The method for evaluating determinant in terms of cofactor is called ______________ expansion. *Laplace* ______________ is a matrix in which every element aij is replaced with its cofactor *Matrix inversion* ______________ is the transpose of a cofactor matrix *Adjoint matrix* The ______________ Provides a simplified method of solving a system of linear equations through the use of determinants *Cramer’s rule* The ______________ Determinant permits testing for functional dependence, both linear and nonlinear. It is composed of all the first order partial derivatives of a system of equations arranged in ordered sequence. *Jacobian* The value of the ______________ determines the size of multiplier Given the the objective and constraint functions as Z = 4x2 - 2xy + 6y2 subject to x+y = 72. What is the value of the multiplier (λ)? *276* Given the objective and constraint functions as Z = 4x2 - 2xy + 6y2 subject to x+y = 72. The value of x & y are 42 and ­­­______________ respectively *30* Given the income equation as C=102+0.7y, I=150-100i, Ms=300, Mt=0.25y and Mz=124-00i. What is the level of interest rate? *i=0.12* Given the income equation as C = 102+0.7y, I = 150-100i, Ms = 300, Mt = 0.25y and Mz = 124-00i. The corresponding level of consumption and investment are ­­­______________ and 138 respectively? *662* Given the income equation as C = 102+0.7y, I = 150-100i, Ms=300, Mt = 0.25y and Mz = 124-00i. The corresponding level of income and money supply are 800 and ______________ respectively? *300* Given the differential function as Y= (3x4+5)6. Using the chain rule the derivative dy/dx for the function is ______________ *72x3(3x4+5)5* Given the function as y=7x3+5x2+12. Find the second order derivative d2y/dx2 *42x+10* If f(x) = x6+3x4+x. find the second order derivative and evaluate it at x=2 *94* Use the rules of implicit differentiation to find dy/dx for the function y=f(x)=x4y6=89. *dy/dx= -2y/3x* Given the total revenue function as TR=30Q-2Q2. The values of marginal revenue MR if Q=4 and Q=5 are ______________ and 10 respectively *14* Given the TR function as R=4000Q-33Q2 and the total cost as C=2Q3-3Q2+400Q+5000 assuming Q>0. What is the profit function (π)? *-2Q3-30Q2+3600Q-5000* The integral of sum or difference of two or more function is the sum or difference of the individual integral. True or False? ______________ *True* he production function q=AKαLβ is a typical ______________ production function *Cobb-Douglas* When the second derivative of any function equals zero, the ______________ occurs *inflection point* In matrix operation, any matrix of 2 by 3 order means ______________ *Two rows and three columns* When the first derivative of an economic model is zero or undefined, the model is therefore ______________ *Critical* The concept of Derivative is about ______________ *Rate of change* Differentiation is a primitive function in calculus. True or False ______________ *FALSE* The integral of sum or difference of two or more function is the sum or difference of the individual integral. True or False? ______________ *True* A continuous function is one which has……………….. in its curve. It can be drawn without lifting the pencil from the paper. No breaks The process of finding the derivative of a function is known as Differentiation A tangent is a straight line that touches a curve at Only one point A function is said to be ………….. at a point if the derivative exists at that point Differentiable ……………….. is a square matrix which has 1 for every element on the principal diagonal from left to right and 0 everywhere else Identity A function f(x) is……….. at x=a if some small region close to the point [a,f(a)] the graph of the function lies completely above its tangent line convex A function f(x) is said to be……….. at x=a if in the immediate vicinity of the point [a,f(a)] the graph of the function rises (fall) as it move left to right. Increasing/decreasing respectively A point at which a function is at relative maximum or maximum is called A relative extremum A point in the domain of a function where the derivative equals zero or is undefined is called a intercept An inflection point is a point on………. Where the function crosses its tangent and changes from concave to convex or vice-versa graph The process of finding the relative maximum or minimum of a function is known as optimization Reversing the process of differentiation and finding the original function from the derivative is called integration In the integration, the original function f(x) is called the Integral or anti derivative Suppose a firm faces a demand curve for its product P = a - bQ, and the firm's costs of production and marketing are C(Q) = cQ + d, where P is price, Q is quantity, and a, b, c, and d are positive constants. Find the second order condition (SOC) for maximum profit d2Π/dQ2 = -2b < 0, Suppose the firm faces a demand curve for its product P = 32 - 2Q, and the firm's costs of production and marketing are C(Q) = 2Q2. Find The price and quantity that maximize profit, and the corresponding value of profit. Q=4, P=24 and Π = 64. respectively ………….. is a rectangular array of numbers or variables or parameters each of which has a carefully ordered place within the matrix matrix The numbers or parameters in the matrix are referred to as……… of the matrix elements The policy that deals with the use of government expenditure and tax to control economic performance is __________ Fiscal The numbers in in a horizontal and vertical line are called……….. Rows and columns respectively The dimension of a matrix is defined by the number of…..…….. Number of rows and columns In a matrix whose number of rows are equals to the number of columns s called…… Square matrix If a matrix is composed of single column such that its dimension is r*1 it is called a……….. Column vector A matrix which converts the rows of A to columns and the columns of A to rows is called……… Transpose of A, A’ Addition and subtraction of Two matrices A&B requires that, the two matrices are of………. Equal dimensions The process of multiplying every element of a matrix by a number is called a………………multiplication Scalar ……………….. is a square matrix which has 1 for every element on the principal diagonal from left to right and 0 everywhere else Identity Given the total cost function as TC=3Q2+7Q+12. Find the MC function MC=6Q+7 Given the total cost function as TC=3Q2+7Q+12. Find the AC function AC= TC/Q= 3Q+7+12/Q Given the total cost function as TC=3Q2+7Q+12. Find the value of MC, when Q= 3 and 5 respectively 25 & 37 respectively Given the total cost function as TC=3Q2+7Q+12. Find the value of AC function when Q=3 and 5 respectively 20 & 24.4 respectively Given that, C=200+0.9Yd, where Yd=Y-T, and T=300+0.2Y, use the derivative to find the value of marginal propensity to consume MPC MPC= dc/dy= 0.72 Given the total revenue function as TR=32Q-Q2 find the critical value and maximum profit at the critical values respectively 16 & 256 respectively Given the TR= 1400Q-6Q2 and TC=1500+80Q. test the first and second order condition for the profit function respectively. Π’= -12Q+1320=0 and Π’’= -12<0 respectively A monopolist faced with two distinct demand functions as Q1= 24-0.2P1 and Q2= 10-0.05P2, where TC=35+40Q. What prices will the firm charge with discrimination? P1=80 & P2=120 RESPECTIVELY A monopolist faced with two distinct demand functions as Q1= 24-0.2P1 and Q2= 10-0.05P2, where TC=35+40Q. What prices will the firm charge without discrimination? Note that without discrimination P1=P2 P=88