Question

Question 4 (40 Marks) Dave receives utility from buying clothes and grocery items (at the ABC shop). His budget is $200. The ABC shop is offering a 325 coupon for every amount spent on groceries that is equal or greater than 1605 To be simple, let the price of clothes be $1 per unit and the price of groceries be $2 per unit. And let Y be the quantity of clothes consumed and X be the quantity of groceries consumed. His utility function is given as 4In X 80 The graph above shows how the budget line will change after the coupon is received when spending 160$ or more on grocery. a. (10 Marks) Find the optimal allocation of X and Y for Dave if his budget is $100 (that is, if he doesn't receive the coupon offer). b. (20 Marks) Find the optimal allocation of X and Y for Dave if his whole budget increases by the value of the coupon. (10 Marks) Does receiving coupon offer make him change his optimal choice for X and Y? Please draw the graph and illustrate your answer. c.

Answer 1

solution & from the aboue guien question (ny) = 7 emy + the enx > Muxteligend =) y = ou y = 2 -) Here Py = $2 - and Py = $1 =) Budget = $100 Budget Conjtraint = 100 = 2x+4 flow MUY MUY Pox? PY - UX=4Y [124]

plugging on to the budget Corybroint 100 = 2x+4 put xx - 100 = 2x+y - 3x = 100 - 8 = 33.3 = 33 unity - Y=333 = 33 unity 2. we will have to find out how much Dave can spend on growries from $200 budget >> Budget Corytreent - 200 - 2x+4 putting & = 7 in to the constraint, =) 200 - 2X+X -) 3X – 200 - x = 66.67 = 67 cenits s) Y 66.67 = 67 units flowe, Consumption of 67 unity measy Spending (6782) = 134$ on groors

bave will no receive any coupon on gooris becauye due to optimal allocation, He is spending $134 on grocerie and Coupon y auailable when $160 is spend. 3. Daf Dalle, spends $160 in Consumption of x. He Consumes to units of Y - Now, with $32 Coupon he can get Additional quantities of Commodity X. (with 32-16 more unity of x can be conjuna 96 > 80