경제원론 관련 문제인데요.

제 답이 맞는지 확신이 가지 않습니다...

특히 4번과 5번의 D는 아예 못풀겠고요..

혹시 제 풀이과정중에 잘못된 것이 있을까요?

 

 

 

 

 

 

 

 

 

 

 

1. Short Answer Question
Draw two straight-line parallel demand curves. Then draw an upward-sloping line through the
origin to intersect both curves. Compare the elasticities at these two points.

2. Answer Questions
Julio receives utility from consuming food(F) and clothing(C) as given by the utility function U(F,C)
= F*C. In addition, the price of food is $2 per unit, the price of clothing is $10 per unit, and Julio's
weekly income is $50.

(a) What is Julio's marginal rate of substitution of food for clothing when utility is maximized?
Explain.

(b) Suppose instead that Julio is consuming a bundle with more food and less clothing than his
utility maximizing bundle. Would his marginal rate of substitution of food for clothing be
greater than or less than your answer in part (a)? Explain.

3. Short Answer Question
There exist two goods, X and Y, which are not giffen goods. The price consumption path
according to change of price of X is derived from the given utility function and the budget
constraint. There are two bundles of goods, (X=8, Y=8), (X=5, Y=6), which lie on the price
consumption path. Compare the MRS of those two bundles of goods.

Ginny consumes two goods, X and Y. She has a utility function given by the following:
U(X,Y)=logX+23logY

The current prices of X and Y are 3 and 2 respectively. Ginny currently has an income of 25 per time period.
(a) Calculate the optimal quantities of X and Y that Ginny should choose, given her budget constraint. Graph your answer.
(b) Derive Engel curve for X and Y, respectively.
(c) Derive demand curves for X and Y.

5. Answer question
Emily's utility function is as follows:
U(x,y)= xy2
x and y represent the consumption on cake and steak, respectively. The price of cake is $20 and the price of steak is $40. And Emily's disposable income is $1000.
(a) Find the optimal consumption bundle.
(b) Derive the Engel curve for cake and steak, respectively and determine whether the cake and steak are normal goods or inferior goods.
(c) Derive the demand curve for cake and steak, respectively.
(d) Assume that the price of steak rose to $60. Numerically calculate the magnitude of the substitution effect and income effect. And graphically illustrate these two effects.