using Lagrangian method to
find the optimal Labor supply
16. Suppose labor demand is given by the equation
L = 50 −2W,
where L is the number of workers and W is the wage rate.
16a. The slope of the demand curve can be viewed as the amount by which L changes for every 1 unit change in W. This can be expressed formally as C SlopeAL ДW. where A refers to a small change in the value of L or W. Using this definition, find the slope associated...
Find the context free Grammar for the following language L = {w ∈ {a, b, c}* : na (w) + nb (w) ≠ nc (w)}.
Determine whether W = -{l. atb a - b : a,beR > is a subspace of R3. La + 3b +5]
Problem 5 Assume that a worker has the Utility Function U(C,L) C "C" refers to consumption in dollars and "L" to hours of leisure in a day. The worker has an offered wage of $10 per hour, 20 hours available for leisure or work per day, and $30 dollars a day from non- labour income. o 8.60 L (a) Find the budget constraint equation of the individual. (b) Find the optimal choice for the individual in terms of units of...
Show that L = {w ∈ {a, b, c}∗ | |w|a = |w|b = |w|c} is not context-free by using the closure properties of the context-free languages. Note: make sure to use the closure properties of the context-free languages.
Explain ur working
4. [6 marks] Using the following graph representation (G(VE,w)): V a, b,c, d,e, fh E -la, b, [a, fl,la,d, (b,ej, [b,d, c,fl,fc,d],Id,el, sd, f) W(a, b) 4, W(a, f)-9, W(a, d)-10 W(b, e) 12, W (b, d)7, W(c,d) 3 a) [3 marks] Draw the graph including weights. b) [2 + 1-3 marks] Given the following algorithm for finding a minimum spanning tree for a graph: Given a graph (G(V,E)) create a new graph (F) vith nodes (V)...
A. L=25; K=16
B. L=40; K=10
C. L=16; K=25
D. L=10; K=40
E. L=20; K=20
= VE Lulu owns a firm that produces leggings. The production function is given by Q=2VKVL, so that MPL K and MPK = Q is Lulu's VL VK output, K is capital, L is labor, and MP is the marginal product. The wage (w)rate per worker (L) is $40 per day and rental rate (r) per unit of capital (K) is $10 per day. How...
9、Let W and L denote the wage and the amount of labor employed, respectively. A firm faces the labor supply curve L = 2W - 6 and the marginal product of labor is given by MPL = 20 - L. The firm sells its output in a perfectly competitive market at $0.50 each. (a) If this labor market is perfectly competitive, find the equilibrium employment, the equilibrium wage, and the number of unemployed people. (b) Suppose that the government imposes...
Let ?= (a, b). The Language L = {w E ?. : na(w) < na(w)) is not regular. (Note: na(w) and nu(w) are the number of a's and 's in tw, respectively.) To show this language is not regular, suppose you are given p. You now have complete choice of w. So choose wa+1, Of course you see how this satisfies the requirements of words in the language. Now, answer the following: (a) What is the largest value of lryl?...
5) (20 pts) For the simply supported beam shown, find the appropriate W-section to support the loads. L- 15 ft, w 400 lb/ft, P 4000 lb, Ơallow = 36,000 lb/in2 L/2 L/2 wL/2 wL/2 Beam size-
5) (20 pts) For the simply supported beam shown, find the appropriate W-section to support the loads. L- 15 ft, w 400 lb/ft, P 4000 lb, Ơallow = 36,000 lb/in2 L/2 L/2 wL/2 wL/2 Beam size-