Question

2. Lisa enjoys apples and grapes. The extent of her satisfaction is revealed by the following utility schedule: Pounds of Total Pounds of Total Apples Utility Grapes Utility 8 units 1 12þ 15 3 24 a) Compute Lisa's marginal utility for each commodity. b) Assume that the price for both apples and grapes is $2 per pound. Given a budget of $6, how many pounds of each should Lisa buy to maximize her total satisfaction? Show the maximum satisfaction formula used to get your answer. c) Now suppose the price per pound of apples is $1, half the price of grapes. With a $6 budget, how many pounds of each commodity would maximize her satisfaction? Justify your answer. d) Based on the above information, plot Lisa's demand curve for apples.

Answer 1

(A) Marginal Utility = Change in Total utility / Change in pounds
Pounds of Apple	Total Utility (TU) of Apple	Marginal utility (MU) of of Apple = Change in Total utility of Apple / Change in pounds of Apple	Pounds of Grapes	Total Utility (TU) of Grapes	Marginal utility (MU)of Grapes = Change in Total utility of Grapes / Change in pounds of Grapes
1	8	8	1	12	12
2	12	4	2	20	8
3	15	3	3	24	4
4	17	2	4	26	2
(B)
Pounds of Apple or Quantity of Apple	Total Utility (TU) of Apple	Marginal utility (MU) of of Apple	Marginal utility (MU) of Apple / Price of of Apple ($2)	Pounds of Grapes or Quantity of Grapes	Total Utility (TU) of Grapes	Marginal utility (MU)of Grapes	Marginal utility (MU) of Grapes / Price of Grapes ($2)
1	8	8	4	1	12	12	6
2	12	4	2	2	20	8	4
3	15	3	1.5	3	24	4	2
4	17	2	1	4	26	2	1
Lisa will attain equilibrium when the ratio of MU of Apple with price of Apple should equal with the
the ratio of MU of Grapes with the price of Grapes
the above condition is satisfied at 1 units of Apple and 2 units of Grapes
MU of Apple / Price of Apple = MU of Grapes / Price of Grapes = 4
Moreover the budget of lisa is given as $6
Budget = ( Price of Apple x Quantity of Apple) + (Price of Grapes x Quantity of Grapes)
Budget = ($2x1) + ($2x2) = $2 + $4 = $6
Lisa will get Maximum utility at 1 units of Apple and 2 units of Grapes
(C)
Pounds of Apple or Quantity of Apple	Total Utility (TU) of Apple	Marginal utility (MU) of of Apple	Marginal utility (MU) of Apple / Price of of Apple ($1)	Pounds of Grapes or Quantity of Grapes	Total Utility (TU) of Grapes	Marginal utility (MU)of Grapes	Marginal utility (MU) of Grapes / Price of Grapes ($2)
1	8	8	8	1	12	12	6
2	12	4	4	2	20	8	4
3	15	3	3	3	24	4	2
4	17	2	2	4	26	2	1
Lisa will attain equilibrium when the ratio of MU of Apple with price of Apple should equal with the
the ratio of MU of Grapes with the price of Grapes
the above condition is satisfied at 2 units of Apple and 2 units of Grapes
MU of Apple / Price of Apple = MU of Grapes / Price of Grapes = 4
Moreover the budget of lisa is given as $6
Budget = ( Price of Apple x Quantity of Apple) + (Price of Grapes x Quantity of Grapes)
Budget = ($1x2) + ($2x2) = $2 + $4 = $6
Lisa will get Maximum utility at 2 units of Apple and 2 units of Grapes
(D) Based on the above information we can prepare a demand schedule of Lisa for Apple
Price of Apple in $	Pounds of Apple
1	2
2	1

In the above diagram the horizontal axis represents the pounds of apple and the vertical axis represents the price of apple in $. The demand curve of Lisa for apple is D (blue colour), indicates 1pounds of apple is demanded when the price of apple is $2 per pound when the price of apple falls to $1 its quantity demanded increases to 2 pounds

(1,2) Price of Apple in Pounds of Apple