3.(POINTS: 40)

Daniel likes to consume his wine paired with cheese in the proportion of 1:2. In fact, his

preferences are represented by:

The current prices of wine and cheese arepw= $10 andpc= $3, respectively. Daniel's income

is $48.

1. (a)What is Daniel's optimal bundle? Present all the necessary calculations.(Points: 5)
2. (b)Draw the budget constraint in the followingwcdiagramand mark the optimal bundle found in the previous questions.(Points: 5)

Assume the price of wine increases to $18.

(c) What is the optimal bundle under the new price? Present all necessary calculations.

(Points: 4)

1. (d)Decompose this price increase into the substitution and income effects.(Points: 8)
2. Hint:The substitution effect captures Daniel's reaction to the change in the price ratio, while the income effect captures the fact that the price increase makes Daniel poorer in general.
3. (e)Considering the new prices, calculate the income Daniel should have in order to be able to afford the intermediate bundle (wsub,csub), found in the decomposition above (denote this incomeIsub).(Points: 3)
4. (f)In the graph above draw:
5. the budget constraint under the new prices and the original income; the budget constraint under the new prices andIsub;
6. mark the optimal choice under the new prices and (wsub,csub)

Daniel likes to consume his wine paired with cheese in the proportion of 1:2. In fact. his preferences are represented by: u(w,c) = min{2w, c} The current prices of wine and cheese are pw = $10 and pc = $3. respectively. Daniel's income is $48. (a) What is Daniel's optimal bundle? Present all the necessary calculations. (Points: 5) (b) Draw the budget constraint in the following we -diagram and mark the optimal bundle found in the previous questions. (Points: 5) Assume the price of wine increases to $18. (c) What is the optimal bundle under the new price? Present all necessary calculations. (Points: 4) (d) Deoompose this price increase into the substitution and income effects. (Points: 8) Hint: The substitution effect captures Daniel '5 reaction to the change in the price ratio, while the income e'ect captures the fact that the price increase makes Daniel poorer in general. (e) Considering the new prices. calculate the income Daniel should have in order to be able to afford the intermediate bundie (Md'd'm''). found in the decomposition above (denote this income I\"). (Points: 3) (f) In the graph above draw: I the budget constraint under the new price and the original income; I the budget constraint under the new prices and I\"; - ma'k the optimal choice under the new prices and (W,c"")