IE545 Homework 2 and Extra Credit 2
October 5, 2014
Due Date: Next Friday (September 26, 2014)
Please submit the homework and extra credit in paper in class. The textbook here refers to
Nicholson 11th Edition.
1. (Problem 2.1 a in the textb
Grade: -see back of this page-
Time: 50 minutes
CLOSED BOOK EXCEPT for two 8.5 11 sheets plus your calculator
Please answer only on test pages, you may use the back side
DO NOT attach ext
A case where the statement will not hold good:
AB is not convex
Statement in EC would be true if a convex set is completely contained in another convex set.
EC 4: It is given tha gi(x) is convex on X = (x|x>=0)
F(x) picks the maxim
HW 1: Extra Credit
3.1) All the graphs were plotted in excel by assigning the utility derived as a constant and finding pairs of
(x,y) that satisfy the utility function. Pairs and x and ys, for a given constant utility are plotted against
each other as sh
Extra Credit 1st November: due next Thursday, 11/03 class time or should be uploaded on blackboard
Referring to the example given in class where:
p= 150 - 0.02q (p=a-bq), TR=pq= 150q 0.02q2 and Let TC= 42,000 + 53q. Calculate the output, q,
HW 5: Extra credit
Given U (m) U ( g , v) min g 2, v .
No matter what the relative prices are (i.e., the slope of the budget constraint), the
maximum utility intersection will always be at the vertex of an indifference curve
where g 2v.
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The constraint is b c 5. Set up the Lagrangian:
L 20c c 2 18b 3b 2 (5 c b).
The first-order conditions are
Lc 20 2c 0
Lb 18 6b 0
L 5 c b 0.
Solving the first two equations yields c 3b 1. So b 3b 1 5, implying b* 1, c* 4, and
U * 79.
Homework 1: due next Thursday, 09/08 class time
Required: problems p. 107 10 points for each part
a. #3.1 (dont have to graph)
b. #3.3 (just show diminishing MRS)
a. #3.1 - Graph the indifference curves
b. Prove: that if A & B are 2 co
(, ) = 3 +
= = = 3
MRS is not diminishing as x increases. Therefore, utility function is not convex.
(, ) = .
1 0.5 0.5
= = 2
1 0.5 0.5
As x increases MRS decreases, therefore utility function has a convex
HW 2: Extra Credit
Setting up the Lagrangian, L x y (0.25 xy ). The first-order conditions are
Lx 1 y
Ly 1 x
L 0.25 xy 0.
So x y. Using the constraint ( xy x 2 0.25) gives x* y* 0.5 and = 2. Note that
the solution is the same here as in Problem 2.3, b