Use the Envelope Theorem to explain the meaning of the Lagrange multiplier in the following equality-constrained optimization problem, max f(x), subject to g(x) = c.
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- In the 1980s, President Reagan based his tax and spending policies on supply side economics. The idea behind supply side economics is the marginal tax rate is so high it discourages work. Cutting the tax rate would end up increasing tax revenue. We develop a simple model of this idea to determine the restrictions on the utility function required to generate a Laffer curve. Let T denote the tax rate, w the real wage rate, and n the labor supply. The tax revenue is T = wNT where wn is labor income, which is the tax base. For convenience, assume w is constant. There is no reason for this assumption to be true, but we impose it to focus on the restrictions on the utility function to generate the Laffer curve. As the tax rate T increases, workers substitute toward leisure and away from consumption. Hence as T rises, wn falls and tax revenue falls for high enough tax rates. Let U,V satisfy the standard assumptions. The model is static and households are endowed with one unit of time. A…In the 1980s, President Reagan based his tax and spending policies õñ supply side economics. The idea behind supply side economics is the marginal tax rate is so high it discourages work. Cutting the tax rate would end up increasing tax revenue. We develop a simple model of this idea to determine the restrictions on the utility function required to generate a Laffer curve. Let t denote the tax rate, w the real wage rate, and n the labor supply. The tax revenue is T = wnT where wn is labor income, which is the tax base. For convenience, assume w is constant. There is no reason for this assumption to be true, but we impose it to focus on the restrictions on the utility function to generate the Laffer curve. As the tax rateT increases, workers substitute toward leisure and away from consumption. Hence as 7 rises, wn falls and tax revenue falls for high enough tax rates. Let U, V satisfy the standard assumptions. The model is static and households are endowed with one unit of time. A…Robinson Crusoe has exactly 12 hours per day to spend gathering coconuts ( C) or catching fish (F). Let tp denote the time (in hours) spent catching fish and tc the time (in hours) spent gathering coconuts per day. Robinson can catch 3 fish per hour or he can gather 6 coconuts per hour; his "production technology" can thus be described by: F = 3tp and C = 6tc. Robinson's utility function is U(F,C) = FC where F is his consumption of fish and C is his consumption of coconuts. 1. (a) Write down Robinson's time constraint and hence find an equation for his Production Possibility Frontier (PPF). (b) Find the number of fish Robinson will catch per day and the number of coconuts he will gather per day.
- Good morning. Please help me to solve this exercise in as much detail as possible. Explaining step by step. This is a mathematical economics exercise that seeks to maximize a function. Thank you very much.Laffer curve In the 1980s, president Reagan based his tax and spending policies on supply side eonomics. The idea behind supply side economics is the marginal tax rate is so high it discourages work. Cutting the tax rate would end up increasing tax revenue. We develop a simple model of this idea to determine the restrictions on the utility function required to generate a Laffer curve. Let T denote the tax rate, w is the real wage rate and n the labor supply. The tax revenue is T=wnT where wn is labor income, which is the tax base. For convinience assume w is constant. There is no reason for this assumption to be true, but we impose it to focus on the restrictions on the utility function to generate the Laffer curve. As the tax rate T increases, workers substitute towards leisure and away from consumption. Hence as T rises, wn falls and tax revenues falls for high enough tax rates. Let U,V satisfy the standard assumptions. The model is static and households are endowed with one unit of…Laffer curve In the 1980s, president Reagan based his tax and spending policies on supply side eonomics. The idea behind supply side economics is the marginal tax rate is so high it discourages work. Cutting the tax rate would end up increasing tax revenue. We develop a simple model of this idea to determine the restrictions on the utility function required to generate a Laffer curve. Let T denote the tax rate, w is the real wage rate and n the labor supply. The tax revenue is T=wnT where wn is labor income, which is the tax base. For convinience assume w is constant. There is no reason for this assumption to be true, but we impose it to focus on the restrictions on the utility function to generate the Laffer curve. As the tax rate T increases, workers substitute towards leisure and away from consumption. Hence as T rises, wn falls and tax revenues falls for high enough tax rates. Let U,V satisfy the standard assumptions. The model is static and households are endowed with one unit of…
- Maximize the function f(x)= x^2/5 (10-2x)^1/3 a. Give maximization problem. b. Give first order conditions for the maximization problem. c. Find the solution to this maximization problem.Define the conditions for a weakly quasi-concave Cobb-Douglas FunctionConsider the following consumption problem commonly referred to as the "cake- eating" problem. The consumer starts with a certain amount of capital, ko (e.g. a certain size for the cake), and "eats" it over time. The consumer's problem is to maximize: 3* log(ct) max t=0 subject to the constraints: ki+1 > k – Ct ko 0 given > a) Write down Bellman's equation for this problem.
- Define Optimization in an indifference curve along with relevant examples?constraint optimization 1. a. use the substitution method. given the production function, Q=5k+3L+2KL, choose the input to maximized output subject to the constraint that the planned expanditure on input is 140 dollars. each unit of labour cost 4 dollars and each unit of capital cost 20 b. use the langrange multiplier given Z=4x2+3xy+6y2, subject to the constraint x+y=56Consider a consumer’s constrained optimization problem. max u(n,y)=4n+3y subject to wn+y=24w+Yo Where N = non-work (leisure) hours, Y = total income (consumption), w = the wage rate and H = hours worked with N + H = 24. a. Assuming an interior solution, use the first order conditions from the Lagrangean to solve for the utility maximizing choice of N* and Y*. How many hours, H*, does this consumer work? (Any of these answers might be functions of w.) when w=1 and Yo=50. No hand written solution and no image