# The theory of individual behavior

A consumer must divide $250 between teh consumption of product X and product Y. The relevant market prices are Px= $5 and Py= $10.

a. Write the equation for the consumers budget line.

b. Illustrate the consumers oppurtuinity set in a carefully labeled diagram.

c. Show how the consumers opportuinity set changes when the price of good X increases to $10. How does this change alter the market rateof subsitution between X and Y?

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#### Solution Preview

Total income is given to be $250.

There are two goods, X and Y. Price of X is Px = $5, and price of Y is Py = $10.

Let Qx and Qy be quantities of X and Y respectively.

a. The general equation for a budget line is:

Px * Qx + Py * Qy <= Income

Putting in the numbers from above we get

5Qx + 10Qy <= 250

b. To determine the consumer's opportunity set we just need to plot this one a graph with good X on one axis and good Y on the other. In the accompanying graph the blue line is the case when the prices are given to be $5 and $10 for X and Y respectively.

To determine where they intersect the axes we need to solve the budget ...

#### Solution Summary

The slope of this graph is assessed.