Consider the function Y = X Z, X, Z 0. a. Graph the Y = 4 contour line for this function. How does

Consider the function Y = X ∙ Z, X, Z ≥ 0.

a. Graph the Y = 4 contour line for this function. How does this line compare to the Y = 2 contour line in Figure 1A.5? Explain the reasons for any similarities.

Contour Lines for Y = √X ∙ Z

b. Where does the line X + 4Z = 8 intersect the Y = 4 contour line?

c. Are there any points on the Y = 4 contour line other than the point identified in part b that satisfy this linear equation? Explain your reasoning.

d. Consider now the equation X + 4Z = 10. Where does this equation intersect the Y = 4 contour line? How does this solution compare to the one you calculated in part b?

e. Are there points on the equation defined in part d that would yield a value greater than 4 for Y?

f. Can you think of any economic model that would resemble the calculations in thisproblem?

9 4 Y=3 Y=2 =1 9