The smarter way
to do assignments.

Please note that this is just a preview of a school assignment posted on our website by one of our clients. If you need assistance with this question too, please click on the Order button at the bottom of the page to get started.

Samantha purchases food (F) and other goods (Y ) with the utility function U = FY, with MUF= Y and MUY= F . Her income is 12. The price of a food is 2 and the price of other goods 1.
a) How many units of food does she consume when she maximizes utility?
b) The government has recently completed a study suggesting that, for a healthy diet, every consumer should consume at least F =8 units of food. The government is considering giving a consumer like Samantha a cash subsidy that would induce her to buy F=8. How large would the cash subsidy need to be? Show her optimal basket with the cash subsidy on an optimal choice diagram with F on the horizontal axis and Y on the vertical axis
c) As an alternative to the cash subsidy in part (b), the government is also considering giving consumers like Samantha food stamps, that is, vouchers with a cash value that can only be redeemed to purchase food. Verify that if the government gives her vouchers worth \$16, she will choose F =8. Illustrate her optimal choice on an optimal choice diagram. (You may use the same graph you drew in part (b).)
Answer : U = FY , MUF= Y,MUY= F, Income (M) = 12 PF = 2 , PY = 1 a) Utility Maximization condition : MRS = MUF/MUY = PF/PY So,MUF/MUY = PF/PY Y/F = 2 or , Y = 2F (i) Budget constraint : 2F + Y = 12 2F + 2F = 12 Using (i) F = 3 and Y = 6 b) Budget Constraint :2F + Y = M Equilibrium condition :Y = 2F So , 4F = M For , F = 8 , Put F = 8 in above equation . We get M = 32 Hence ,cash subsidy need to be \$20 (32 – 12). So , we have , F = 8 , Y = 16 and M = 32 As shown , Our budget line is OADand optimal point is Awhere indifference curve intersects budget line. c) Government give food stamps of\$16 that can be only redeemed on food. Hence , As PF = \$2 , Samantha can purchase 8 (16/2) units of food….

ce , His new utility function : (f+8)Y (As total Food (F) =f+ 8 i.e funits purchased by her income and 8 units by food stamps) MRS = MUF/MUY = Y/f+8 Equilibrium condition : MRS = PF/PY Y/f+8 = 2 or, Y = 2f+ 16 Budget constraint : 2f+ Y = 12 2f+2f+ 16 = 12 or , f= -1 , Which is not possible , Hence f= 0 Therefore , F = 0 + 8 = 8 So, We have , F = 8 and Y =12 As shown , Our new budget line is CBE and optimal point is B where indifference curve intersects budget line

## GET HELP WITH THIS ASSIGNMENT TODAY

Clicking on this button will take you to our custom assignment page. Here you can fill out all the additional details for this particular paper (grading rubric, academic style, number of sources etc), after which your paper will get assigned to a course-specific writer. If you have any issues/concerns, please don’t hesitate to contact our live support team or email us right away.