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ECON 412 - Penn State University Labor Economics and Labor Markets Homework 2 Ewout Verriest Fall 2020 Problem 1 Consider a firm which produces according to the following production function: q = A( √ E + √ K) where q denotes output, E denotes the number of workers hired by the firm, K denotes capital, and A > 0 is a technology parameter. The marginal product of labor is therefore given by MPE = A 2 √ E . In the short run, the firm rents 100 units of capital, at a ren...

15–312: Principles of Programming Languages Midterm Examination (Sample Solutions)

CMPSC 461: Programming Language Concepts Assignment 6 Solution Problem 1 [8pt] Prove that the following two Hoare triples are valid. (Hint: in predicate logic P1 ⇒ P2 is equivalent to ¬P1 ∨ P2). a) (4pt) {x > −1} y := x * 2; y := y + 3; {y > 0} Solution: wp(y:=x*2;y:=y+3, y > 0) = wp(y:=x*2, wp(y:=y+3, y > 0)) = wp(y:=x*2, y + 3 > 0) = x ∗ 2 + 3 > 0 Moreover, the precondition

CMPSC 461: Programming Language Concepts Assignment 1 Solution Problem 1 [6pt] Add parentheses to the following lambda terms so that the grouping of sub-terms becomes explicit. For example, the term λx. x λy. y with parentheses is λx. (x (λy. y)). a) (3pt) λx. λy. x y z Solution: λx. (λy. ((x y) z)) b) (3pt) λx. λy. (λx. x x) y λz. x z Solution: λx. (λy. (((λx. (x x)) y) (λz. (x z)))) Problem 2 [6pt] Fully evaluate the following λ-term so that no further β-reduction is ...

CMPSC 461: Programming Language Concepts Assignment 4 Solution Problem 1 [5pt] Give an example in a programming language that you’re familiar with in which a variable is alive but not in scope. Solution: One example in C. After the function exists, the object that C links to is no longer in scope, but it is alive. 1 void foo() 2 { 3 myClass* C = new myClass(); 4 return; 5 } Problem 2 [10pt] Consider the following class instances in a C++ program: 1 static myClass A; 2 3 int main(...

CMPSC 461: Programming Language Concepts Assignment 5 Solution Problem 1 [9pt] Consider the following C program: int SumOfSquares(int n) { if (n <= 0) return 0; else return n*n+SumOfSquares(n-1); } a) (5pt) Write down a tail recursive implementation of function SumOfSquares in C language. You can use helper function in your solution. Solution: int SumOfSquares(int n) { return SumOfSquaresHelp(0, n); } int SumOfSquaresHelp(int a, int n) { if (n <= 0) return a; else return...

Programming Language Concepts CMPSC 461, FALL 2018 Midterm #1 Solution This exam is closed book, closed notes. You may not use any additional materials during the exam. All electronic devices must be put away. You may have nothing on your desk except this exam and writing instruments. The exam consists of 8 questions and 1 bonus question on 4 pages, totaling 100 points + 10 bonus points. Read each question carefully and use your time judiciously. The problems are not ordered by their dif...

CMPSC 461: Programming Language Concepts Assignment 6 Solution Problem 1 [6pt] Assume that integers are stored using one byte in memory. What are the binaries for 8 and -10 in two’s complement format? What is the result of (8-10) in two’s complement format? Solution: binary for 8: binary for -10: result of (8-10): Problem 2 [10pt] Consider the following C declaration: union U1 {int a; float b;}; union U2 {char a; double b;}; struct S { union U1 u1; union U2 u2; } s; Assume ...

Programming Language Concepts CMPSC 461, FALL 2018 Midterm #2 Solution P# Possible Score 1 8 2 10 3 16 4 8 5 24 6 16 7 10 8 8 Bonus 10 Total 110 This exam is closed book, closed notes. You may not use any additional materials during the exam. All electronic devices must be put away. You may have nothing on your desk except this exam and writing instruments. The exam consists of 8 questions and 1 bonus question on 5 pages, totaling 100 points + 10 bonus points. Read each questio...