8.2 Suppose that ,* f(x) dx = 6, 8* g(x) dx = 4, and S f(x) dx = 2. Evaluate the following integrals: a. -S2f(x) dx (2 Marks) b. Si(3f(x) – 2g(x)) dx (2 Marks) c. $*f(x)g(x) dx (2 Marks) d. S@dx (2 Marks) [Sub Total 20 Marks]
Suppose a consumer values income (m) and leisure (l) with utility function U(m,l)=ml. The consumer has T hours per week to allocate between labor and leisure with an hourly wage rate of w. The consumer's weekly time constraint is (m/w)+l=T. Use a Lagrangian to maximize the consumer's utility subject to the weekly time constraint. What is the optimal amount of leisure? what is the optimal amount of labor (L=T-l)
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integral dy dx into an integral over G, and evaluate both integrals a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then...
3. A taxpayer has utility function U(x, L) = x ^1/2 − L where L is hours of labour supply and x is consumption. The taxpayer earns a wage of $4 per hour worked (which is fixed throughout the analysis). (a) Suppose that the government imposes a proportional (percentage) tax at rate τ on labour income, so that the taxpayer’s budget constraint is x = (1 − τ )4L. Solve for the optimal labour supply (L) and consumption (x) as...
Help on number 2 A-C Math 166 Spring 2020 Lab 12 - Integration Strategies and Improper Integrals 1. Evaluate the following integrals. (a) | In(x2 + 2a) dx 100 dx (8) Jo Je to (1) ["* sin(a) Vsee(2) de 5 1 11 x² – 2x – 3 dx 87/2 13 x(lnx)2 de (c) / tarda (1) [4x*e*** de 2. For what values of p do the following improper integrals converge? (1/2 da (0) Le 2 In () Jo 3. Give...
A consumer must maximize utility, U-for.y), subject to the constraint that she spends all her income, M on purchasing two goods x, y. The unit prices of the goods, p, and py respectively, are market determined and hence exogenous (3 marks) (3 marks) rKS rice marks) (i e1 (2 marks) 0.8,0.2 (d) Let the utility function be U -5x ф Solve the maximization problem in this case (that is obtain x*, y*, 8y0.z and unit prices pr - p- 1...
H=1.68 T=26 F=2 L=2 S=30 11) Determine the extrema of g(u,v) = Hu-(F+L)t/2 subject to the constraint x2+y2= S*H Ans.
Suppose that f(2) = -3, 9(2) = 4, f'(2) = -5, and g(2) = 1. Find h'(2). (a) h(x) = 3f(x) - 2g(x) h'(2) h(x) = f(x)g(x) (b) h'(2) (c) h(x) = f(x) g(x) h'(2) (d) h(x) g(x) 1 + f(x) h'(2)
A consumer must maximize utility, U-f(x.y), subject to the constraint that she spends all her income, M on purchasing two goods x, v. The unit prices of the goods, px and py respectively, are market determined and hence exogenous. (i) State the objective function, constraint, and choice variables of this problem (3 marks) (ii) Obtain the Lagrangean for this problem, using λ to represent the Lagrange multiplier. (3 marks) (i) Obtain the first order conditions of this problem in terms...
Find the extreme values of the function f(x, y) = 3x + 6y subject to the constraint g(x, y) = x2 + y2 - 5 = 0. (If an answer does not exist, maximum minimum + -/2 points RogaCalcET3 14.8.006. Find the minimum and maximum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.) f(x, y) = 9x2 + 4y2, xy = 4 fmin = Fmax = +-12 points RogaCalcET3 14.8.010. Find...