Sally can work any number of hour she chooses at a wage of dollars per hour. She

Question

Sally can work any number of hour she chooses at a wage of dollars per hour. She values consumption, C, and also hours of leisure (the hours she is not working), H, in dollars. The hours she works per day is 24 - H. Sally's MRS is given by 2C/H. Write the equation for Sally's budget constraint. What two conditions define Sally's optimal choice of C and H? Solve for sally's optimal choices of C and H. Does the optimal H vary with w? What happens to the number of hours Sally works if the government introduces a tax t on her wage income, so that the wage she actually takes home is now(1 - t)w?

Explanation / Answer

wage rate = $w per hour consumption = $C hours of leisure = $H per day working hrs = 24-H MRS = 2C/H i) Budget constraint Y = w*(24-H) ii) the two conditions are 1. budget constraint Y=w*(24-H) 2. MRS = 2C/H iii) assuming that income is going in consumption then, C=w*(24-H) --1 MRS = dH/dC = 2C/H --2 differentiating 1 wrt to H we get dC/dH = -w equating this wth equation 2 we get H = -2*w*C H= -2*w*(w*(24-H)) on solving H = 48*w^2/(2w^2-1) similarly C=w*(24-H) = 24*w/(1-2*w^2) yes the optimal H vary with w iv) wage actually received is (1-t)w therefore new H* = 48*[(1-t)w]^2/(2[(1-t)w]^2 - 1) since (1-t) is positive we conclude that new H*

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