Hi, Could you help me solve this problem? The problem is a continuance to an ”efficient output ” based on a social planner’s problem, where it was compared to the output in the market equilibrium with monopolistic competition.The problem:Now consider the social planner’s problem in the context of labour supply and income taxation and compare the solution to it to a market equilibrium with potentially distortionary taxation. The rest of the problem is attacteh ad an image. The problem of a representative household (representing aggregate labour supply) is tochoose consumption c and hours worked h to maximizelog(c) +log(1)subject toandC = = (1 – t)whh+1= L,where I denotes leisure, w wage rate, 0 < t < 1 income tax rate, and L > 0 fixed time en-dowment.=Aggregate output is determined as Y Ah, where A > 0. The government budget constraintis twh = G, where G> 0 denotes government consumption, and the aggregate resourceconstraint isY = c + G.In the market equilibrium, the labour market is competitive and hence w = A.i) Derive hours worked (as a function of the parameters of the model) in the market equili-brium where hours worked solve the problem of the representative household above and thetax rate is set so that the government budget constraint is satisfied. You should focus onlyon cases where G is small enough so that private consumption c is always strictly positiveand G in the market equilibrium can be financed with tax rate t < 1.ii) Then formulate the problem of a social planner that takes G as given and maximizeshousehold welfare subject only to the aggregate resource constraint and the time constrainth+ 1 = L and use it to derive socially optimal hours worked. Also compare the solution tomarket equilibrium.

i) Derive hours worked in the market equilibriumGiven the utility function:Taking the first order…

i) Derive hours worked (as a function of the parameters of the model) in the market equili- brium where hours worked solve the problem of the representative household above and the tax rate is set so that the government budget constraint is satisfied. You should focus only on cases where G is small enough so that private consumption c is always strictly positive and G in the market equilibrium can be financed with tax rate t < 1. ii) Then formulate the problem of a social planner that takes G as given and maximizes household welfare subject only to the aggregate resource constraint and the time constraint h+ 1 = L and use it to derive socially optimal hours worked. Also compare the solution to market equilibrium.

i) Derive hours worked (as a function of the parameters of the model) in the market equili- brium where hours worked solve the problem of the representative household above and the tax rate is set so that the government budget constraint is satisfied. You should focus only on cases where G is small enough so that private consumption c is always strictly positive and G in the market equilibrium can be financed with tax rate t < 1. ii) Then formulate the problem of a social planner that takes G as given and maximizes household welfare subject only to the aggregate resource constraint and the time constraint h+ 1 = L and use it to derive socially optimal hours worked. Also compare the solution to market equilibrium.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 3E

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