please explain and draw any revalent diagram to support.

Q6. Assume an individual has a utility function of this form

This utility function implies that the individual's marginal utility of leisure is 2C and her marginal utility of consumption is 2L where C and L represent the amount of consumption good and hours of leisure, respectively.The individual has an endowment of V dollars in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume also that this individual has to pay 25 % labour earnings tax to the government.

a)How much utility does the individual receive if she consumes C = 5 and works h = 7 hours?

(4 points)

b)Write down and graphically indicate the budget constraint of the individual. Let p=price of consumption good and w=before tax wage rate.

(6 points)

c)Assume the price of each unit of consumption good p = 15 and the before tax wage rate for each hour of work w = 16, and V = 30 dollars. What is the optimal amount of consumption and leisure?

(12 points)

d)Assume a cash grant welfare program is instituted which pays M = 45 dollars for individuals who do not work. Compute the new optimal labour supply for this individual under the welfare program. Assume that prior to the welfare program, p = 15, w = 16, and V =30 (as in part c). Does the individual accept the welfare program and not work? Show why or why not.

(8 points)