Suppose that in a one-period closed-economy model the representative consumer has the utility function: U(cl) =In(c)+0.8ln(1). The production function is: Y=zN (no capital). The government levies a lump-sum tax (T) on the consumer, and h>G/z. Calculate the government expenditure multiplier.
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- A closed economy one-period macroeconomic model with a government taxing a lump-sum tax Consider the following utility function for the representative consumer U(c,l) = 2Vc - a(1–1)1.5 s.t.c = wN-T 1.5 Where /is leisure, c es consume, N is the total time dedicated to work, l=1-N, T is the lump-sum tax, so government purchases equal taxes G=T, w is wage, and it has the following production function with K fixed and equal to 1 Y = zN°,5 zN0,5 Find the Labor supply curve Ns, labor demand curve Nd, and the optimum wageASAP Suppose the consumer has the utility function U(C,l)=0.5 √C+√ l and has h = 24 hours available, some of which are used as leisure (l) and some supplied to the labor market (NS). Hours of work are paid at the real wage w. The profit income is π = 15. The consumer pays no tax. Writedown the budget constraint and the maximization prob- lem (a Lagrangian) and find the first order conditions for the consumer. Find an expression for the quantity of labor suppliedc) If the value of timber is the following increasing function of time: V = 2t Expressed in units of Rs. 1000. Assuming a discount rate of r and also assuming zero upkeep cost during the period of timber growth, what is the optimal time to cut the timber for sale? Calculate optimal time for r = 5% Question 03. a) Maximize the utility function U = X0Y025 subject to budget constraint 680 = 8X + 5Y Also show that above utility function is homogenous and homothetic. 5P+ P? and b) Find the demand function Q =f (P) if elasticity of demand is - Q = 500 when P = 10 c) Write down the first order and second order conditions for maximum and function y = f(x1, X2, X3,.......... Xn). minimum of a
- Consider a one good, two-period closed economy without government. The representative agent is endowed with ?1 in the first period and ?2 in the second period. (Q) Derive the optimal consumption and investment plans for the representative consumer and representative firm respectively.Consider the model where an individual has wealth k which they can either save or consume. If they save it, they receive a fixed and exogenous return r. The instantaneous utility function is given by: u(c, k) = c + a(k) where c is consumption, k is wealth, and a(k) is a function that defines the utility that an individual gets from holding wealth. The growth in wealth is given as the returns on wealth rk, plus income from working z(t), minus consumption c(t). a. Write out the differential equation for wealth. b. For an infinite time model, set up the optimal control problem with discounting at a rate 8. c. Write the current-valued Hamiltonian of this problem. d. Derive the steady-state level of consumption.For part 1b, my Professor said the answer is $56 but I'm finding it to difficult to get 56. Can you help? Thanks a lot! Jack is the owner of the only local bar in a small town.He sells whiskey in one-ounce glasses. For simplicity, let’s assume it doesn’t cost Jack anything to run his business. There are two customers, Adam and Burt who are twin brothers. Adam’s demand function is yA = 16 – 2p, and Burt’s demand function is yB = 8 – p (price is measured in dollars and quantity is measured by ounces). Jack knows their demand functions, but the problem is that he cannot tell them apart since they look exactly the same to him. To increase his profits, Jack offers the following two options that his customers can choose from: (1) You can pay $T1 up front and drink as much as you want; or (2) Pay $T2 up front and the price per ounce of whiskey will be $p. 1.a If p = 4, what is the maximal T2 that Jack can charge so that Burt is willing to come to the bar? 1.b What is the maximal T1 that…
- 2. Use the budget constraint to replace c in the first-order condition to obtain a single equation that relates the household's choice of I to w and T. 3. Suppose that the government uses all the tax revenue to hire emergency front-line health workers to help during the COVID-19 pandemic. The government pays these workers the prevailing wage rate. How much time (in units) can the government afford to purchase from the workers? Denote this number by m.Consider a two-period endowment economy with a single representative agent. That agent's utility function is: U = In(ct) + (1/2)In(Ct+1) In this endowment economy, output is 100 in period t and 150 in period t+1. What is the equilibrium interest rate (r) in this economy? Write your answer as a percentage, but omit the percent sign. So if you think r=0.1, that's 10%, but write 10. Similarly, if you think r = 1.5, that's 150%, but write 150.Consider a one period model in which a representative agent maximises the utility function: U(c,l) Inc + 5lnl subject to the budget constraints: c = (1-t)w(1-1) + v where c is consumption and is the amount of leisure, they enjoy out of a total of one unit of time available, t is the tax on wage earnings which pays for v in government transfer payments. nt. W d) Derive the equation that determines how much revenue the government will receive for a given rate of tax t. What is this relationship called? e) Solve for the maximum amount of revenue the government can raise from this tax. Hint: the tax rate will be a fraction between 0 and 1. f) In general, what explains the shape of the Laffer curve? g) In this particular example, what are the contributions of the income and substitution effects?
- Consider a one period model in which a representative agent maximises the utility function: U(c,l) Inc + 5lnl subject to the budget constraints: c = (1-t)w(1-1) + V where c is consumption and is the amount of leisure, they enjoy out of a total of one unit of time available, t is the tax on wage earnings which pays for v in government transfer payments. a) Solve for first order conditions of the representative agent. b) Write down the market clearing condition (resource constraint) for the aggregate economy. c) Solve for equilibrium consumption and labour choices. d) Derive the equation that determines how much revenue the government will receive for a given rate of tax t. What is this relationship called? e) Solve for the maximum amount of revenue the government can raise from this tax. Hint: the tax rate will be a fraction between 0 and 1. f) In general, what explains the shape of the Laffer curve? g) In this particular example, what are the contributions of the income and…1. Consider the deterministic Brock-Mirman model studied in class. The discount factor is β ∈ (0, 1), the per-period utility function is u(c) = log(c) and the production function is f(k) = kα + (1 − δ)k, where δ = 1 and α ∈ (0, 1). Assume β = 0.99 and α = 0.3. (a) Compute the model's steady-state k∗. (b) Use the F and G that we derived in class by solving the Bellman equation by guess and verify to plot the optimal decision rules for k and c in the range [0.005, ¯k], where ¯k is the upper bound on the state space. Can you figure out such ¯k. If not, set ¯k to twice the steady-state capital stock. (c) Let the initial capital stock be k0 = 0.5k∗. Compute the time series for kt, t = 1, 2, ..., 200. Plot the time series. Now do the same for k0 = 1.5k∗. Do the sequences converge to k∗? 2. Now solve the model in question (1), with the same parameter values, by…Bob and Ray are thinking of buying a sofa. Bob's utility function is Ug(S, MB) = (1 + S) Mg and Ray's utility function is UR(S, MR) = (4 + S)MR, where S= 0 if they don't get the sofa and S = 1 if they do and where MB and MR are the amounts of money they have respectively to spend on their private consumptions. Bob has a total of $800 to spend on the sofa and other stuff. Ray has a total of $4,000 to spend on the sofa and other stuff. The maximum amount that they could pay for the sofa and still arrange to both be better off than without it is $1,200. $2,200. $650. $1,800. $1,000.