Given two goods x and y with prices px and py and a budget B,

(a) determine the slope-intercept form of the equation for the isocost curve. Using the information from (a), indicate what will happen to the graph of the curve

(b) if the budget changes,

(c) if px changes, and

(d) if py changes.

(a) Starting with the standard form and solving for y,

This is the familiar slope-intercept form of a linear equation y = mx +

b, where m = −(px/py) = the slope and b = B/py = the y coordinate of the y intercept. The y intercept of the isocost line, therefore, is (0, B/py), and as the x intercept of the standard form is (−b/m, 0), the x intercept of the isocost line is [−(B/py)/(−px/py), 0] = (B/px, 0).

(b) From (2.8) it is clear that a change in the budget B will affect the x and y intercepts but not the slope. This means that the isocost curve will shift parallel to the original curve; to the right for an increase in B and to the left, for a decrease in B.

(c) If px changes, the slope –px/py and the x intercept (B/px, 0) will change, but not the y intercept (0, B/py). The graph will get steeper for an increase in px and flatter for a decrease in px, pivoting around the same y intercept.

(d) For a change in py, the slope –px/py and the y intercept (0, B/py) will change, but not the x intercept (B/px, 0). An increase in py makes the y intercept lower and the slope flatter. A decrease in py makes the y intercept higher and the slope steeper. In both instances the x intercept remains the same.

Transcribed Image Text:

Px x+Py y = B Py y (Px x) + B P.x B y = x + (2.8) Py Py