Question

Extend the model of public good. Suppose that output is produced, as in the simplified model with proportional taxation, only with labour and that z=1. Here, however, there is lump-sum taxation, and the PPF is given by Now the consumer has preferences over three goods: private goods C, public goods G, and leisure I. Assume that C and I are perfect complements for the consumer, that is, the consumer always wants to consume C and I in fixed proportions. Suppose that public goods and private goods are perfect substitutes.

What is the optimal choice of leisure and consumption for the representative consumer?

Answer 1

THE OPTIMAL CHOICE OF LEISURE AND CONUPTION FOR THE REPRESENTATIVE CONSUMER IS WHEN THEY ATTAIN THE SITUATION OF ,

N+L=1

WHERE, N= NUMBER OF HOURS IN A WEEK THAT A CONSUMER IS WORKING

AND L = NUMBER OF HOURS OF LEISURE

AND ONE UNIT REPRESNENTS THE TOTAL HOURS

AS THE CONSUMPTION IS DIRECTLY PROPORTIONAL TO THE WAGE YOU GET BY WORKING SO THUS RELATED TO CINSUMPTION,

AND THE OPTIMAL CHOICE IS WHEN THE THE CURVE IS TANGENT TO THE BUDGET CONTRAINTS

AND THERE WE CALCULATE THE OPPORTUNTY COST OF GIVING THE PRIVATE GOODS FOR THE PUBLIC GOODS.

AND THE WAGE RATE AFTER TAX DEPICTS THE SLOE OF CONSUMPTION AND THE LEISURE.