Intermediate Microeconomics: A Modern Approach, Seventh Edition

14.04 Midterm Exam 1 Prof. Sergei Izmalkov
Wed, Oct 1
, y
t
) for t = 1 , . . . , N be a set of observed choices that satisfy WAPM, let Y I and Y O be the
inner and outer bounds to the true production set Y . Let π
+
( p ) , π ( p ) , and π
−
( p ) be pro fi t functions
associated with Y O , Y , and Y I correspondingly.
(a) Show that for all p , π
+
( p ) ≥ π ( p ) ≥ π
−
( p ) .
(b) If for all p , π
+
( p ) = π ( p ) = π
−
( p ) , what you can say about Y O , Y , and Y I ? Provide formal
arguments.
(c) For ( p
1
, y
1
) = ([1 , 1] , [ − 3 , 4]) , and ( p
2
, y
2
) = ([2 , 1] , [ − 1 , 2]) construct Y I and Y O (graphically).
What can you say about returns to scale in the technology these observations are coming from?
Hint: think y = ( − x, y ) .
t
1. Let ( p
2. Given the production function f ( x
1
, x
2
, x
3
) = x
1
min { x
2
, x
3
}
a
striction you have to impose on a ?
a
(a) Calculate pro fi t maximizing supply and demand functions, and the pro fi t function. What re-
(b) Fix Calculate conditional demands and the cost function ( ) y c w , w , y . .
1 2
,
y
(c) Solve the problem py − c ( w
1
, w
2
, y ) → max , do you obtain the same solution as in 2 a ? Explain