>Public econ expenditure analytic questionsanswer the following analytic questions in realtime within 1h. Analytical question 1: Joanne is a low-income single mother. She has 2000 hours per year which she can allocate to either work (H) or leisure (L) so H+L = 2000. If Alex works she receives an hourly wage of $9. She spends all her income on food (F) which costs $2 per unit. The government runs a TANF program with a benefit guarantee of $3000 and a benefit reduction rate of 2/3. a) How many hours H* does she have to work to become ineligible for the program? H* = ( ) b) How much food can she buy when working H* hours? F = ( ) c) Complete the following piecewise function for Joanne’s effective wage: Effective wage =( ) H=H* d) Joanne’s utility function is given by U(LF) = 10ln(L) + 30ln(F). Suppose that she does NOT participate in TANF. Find her optimal bundle (L* F*). (Note: the first derivative of ln(x) with respect to x is 1/x) L* = ( ) F*= ( ) e) Now suppose the government reforms the program by decreasing the benefit guarantee to $2000 (and making no change to the benefit reduction rate). After this change how many hours does Joanne have to work to become ineligible for TANF? H = ( ) f) Describe one reason the government may have for deciding to reduce the benefit guarantee. g) Suppose Joanne does NOT participate in TANF when the benefit guarantee is $3000 (prior to the reform). Consider what happens to her choice of leisure (L) when the benefit guarantee is reduced to $2000. What is the direction of the substitution effect on L for Joanne? (Positive negative zero or ambiguous). Substitution effect direction = () What is the direction of the income effect on L for Joanne? (Positive negative zero or ambiguous). (Positive/negative/zero/ambiguous). Income effect direction =( ). h) Consider a different mother Sarah who also has 2000 hours and faces an hourly wage of $9 but who has a different utility function than Jane. Sarah participated in TANF when the benefit guarantee was $3000 but no longer participates when the benefit guarantee is reduced to $2000. What is the direction of the substitution effect on leisure for Sarah? (Positive/negative/zero/ambiguous).