Question

The derivation of the isorevenue is similar to the derivation of the isocost line. Derive the algebraic equation for the isorevenue line. Explain significance of the intercept and the slope of the isorevenue line.

Answer 1

An isorevenue line shows various combinations of two products which yield same level of revenue. Consider two products X and Y and their respective price P_x and P_y. Hence, total revenue that can be generated is given by P_xX+P_yY=R. So along an isorevenue line, all points will generate a revenue of amount R. All combinations below this line will generate revenue which is less than R and all points above the isorevenue line are infeasible. The equation can be equivalently represented as:

P_yY=R - P_xX => Y = (R/P_y) - (P_x/P_y)X, where (R/P_y) is the intercept of the isorevenue line and [- (P_x/P_y)] is the slope of the isorevenue line. Note that a higher R means higher intercept and hence the isorevenue line shifts to right and vice versa. The intercept can also be interpreted as the maximum level of Y that can be produced with zero production of X. While change in R causes parallel shift of isorevenue line, the relative prices of the product changes the slope of the line.

Isorevenue lines are useful to maximize revenue given the production possibilities curves. The revenue is maximized where the isorevenue line is tangent to the production possibilities curve.