Intermediate MicroEconomics
Aqsa Kiran
Prof. Moinul Islam
7th Feb, 2015
Intermediate Microeconomics
PPE-3100
Home Work -1
1. Suppose a teenager has $20 and likes both rap music (R) and country music (C) with a set of preferences so that U = C1/2R1/2. Suppose that the iTunes price of a rap music song is and the price of a country music song is. Find optimum levels of R and C. What is the greatest level of affordable utility (Use Lagrange method)?
U = C^1/2 R ^1/2
Constrain = Pc +PR = 20
Applying Lagrange Method
L = C^1/2 R^1/2 +
2. Determine whether the following utility functions have strictly convex indifference curves (Use diagram and/or calculus).
a. U= x11/2 + x21/2
b. U= min(x1/5, x2/2) c. U=( x1 + x2)3
3. Consider the following utility functions ((Use diagram and/or calculus ).
a. U= x14 x24
b. U= x11/4 x21/4
c. U = 5x1+3x2
i. Find MRS for each function ii. Graph the indifference curve for U= 1 for each utility function
. iii. Check for convexity/strict convexity, monotonocity/strict monotonocity) axioms. iv. Compare between MRS of (a) and (b), and comment.
4. Suppose a cup of coffee at the campus coffee shop is $2.50 and a cup of hot tea is $1.25.
Suppose a student’s beverage budget is $20 per week. Suppose the student simply prefers more caffeine to less and that the tea sold has exactly one-third the caffeine as the coffee. Find the students optimal bundle and the maximum utility level.
Prof. Moinul Islam
7th Feb, 2015
Intermediate Microeconomics
PPE-3100
Home Work -1
1. Suppose a teenager has $20 and likes both rap music (R) and country music (C) with a set of preferences so that U = C1/2R1/2. Suppose that the iTunes price of a rap music song is and the price of a country music song is. Find optimum levels of R and C. What is the greatest level of affordable utility (Use Lagrange method)?
U = C^1/2 R ^1/2
Constrain = Pc +PR = 20
Applying Lagrange Method
L = C^1/2 R^1/2 +
2. Determine whether the following utility functions have strictly convex indifference curves (Use diagram and/or calculus).
a. U= x11/2 + x21/2
b. U= min(x1/5, x2/2) c. U=( x1 + x2)3
3. Consider the following utility functions ((Use diagram and/or calculus ).
a. U= x14 x24
b. U= x11/4 x21/4
c. U = 5x1+3x2
i. Find MRS for each function ii. Graph the indifference curve for U= 1 for each utility function
. iii. Check for convexity/strict convexity, monotonocity/strict monotonocity) axioms. iv. Compare between MRS of (a) and (b), and comment.
4. Suppose a cup of coffee at the campus coffee shop is $2.50 and a cup of hot tea is $1.25.
Suppose a student’s beverage budget is $20 per week. Suppose the student simply prefers more caffeine to less and that the tea sold has exactly one-third the caffeine as the coffee. Find the students optimal bundle and the maximum utility level.