Suppose you have $120 to spend on food and clothing. The price of food is $4 and the price of...

a. Graph your budget constraint; calculate the slope of it

Let food be F and clothing C such that the budget constraint is expressed as follows:

{eq}$4F + $8C = $120 {/eq}

{eq}F = $30 - 2C {/eq}. The graph of this budget constraint is given as follows:

The slope of the equation can be computed as {eq}\frac{\Delta F}{\Delta C} = -2 {/eq}

b. Briefly explain why your optimal choice is the point at which your budget constraint is tangent to an indifference curve.

When maximizing utility, the consumer is constrained by the budget constraint. For any bundle that the consumer chooses to derive utility from, their total expenditure cannot exceed the budget. Since the consumer is rational, they will prefer to consume at a higher indifference curve. Utility is only maximized when the budget constraint curve and indifference curve and as the consumer chooses a higher indifference curve, the highest indifference curve is the one that is tangent to the indifference curve. It is the point when the slope of the budget constraint is equal to the slope of the indifference curve. It is the point where marginal rate of substitution of one good for another equals the ratio of their prices. That is, {eq}MRS_{xy} = \frac{P_X}{P_y} {/eq}