The diagram above shows an indifference map and the prices and income of a consumer. 1) Determine this budget line. 2) Illustrate the consumer equilibrium position.

The Y-intercept represents the maximum quantity of Good Y that can be purchased if all income is spent on Good Y. \text{Y-intercept} = \frac{\text{Income}}{\text{P}_y} = \frac{$10}{$1.00} = 10 \text{ units of Good Y}

The X-intercept represents the maximum quantity of Good X that can be purchased if all income is spent on Good X. \text{X-intercept} = \frac{\text{Income}}{\text{P}_x} = \frac{$10}{$2} = 5 \text{ units of Good X}

The budget line equation is $\text{P}_x \cdot \text{X} + \text{P}_y \cdot \text{Y} = \text{Income}$.
Substituting the given values:

The budget line is a straight line connecting the Y-intercept (0, 10) and the X-intercept (5, 0).

Consumer equilibrium occurs at the point where the budget line is tangent to the highest attainable indifference curve. From the diagram and the accompanying text, this point is labeled E.

The text explicitly states: "The Consumer in Equilibrium is purchasing 4 units of good y and three units of good x".
Therefore, at equilibrium point E, the consumer purchases:

• Good X: 3 units
• Good Y: 4 units

At the equilibrium point E, the slope of the budget line is equal to the slope of the indifference curve ($\text{IC}_2$). This means the Marginal Rate of Substitution ($\text{MRS}_{XY}$) is equal to the price ratio ($\frac{\text{P}_x}{\text{P}_y}$).

\text{MRS}_{XY} = \frac{$2}{$1} = 2 At equilibrium, the consumer is maximizing their utility given their budget constraint.