Final answer:
With a $3000 income, the horizontal intercept is 600 units of good X and the vertical intercept is 3000 units of the composite good. The slope of the budget constraint is -0.2, reflecting the trade-off between the two goods.
Step-by-step explanation:
To model a consumer's choice between a product good X and a composite good, we can draw a budget constraint that illustrates the feasible set of choices for a given period. If the consumer has a disposable income of $3,000 and the price of good X is $5.00 per unit, the budget constraint can be graphically represented with good X on the horizontal axis and the composite good on the vertical axis.
On the horizontal axis, the maximum number of units of good X that can be purchased without buying any composite goods would be $3000 divided by the price of good X, which is $5 per unit. This calculation yields a maximum of 600 units of good X. This point would be the horizontal intercept.
Similarly, since the price of the composite good is $1 per unit, the vertical intercept would be 3,000 units of the composite good, assuming the consumer spends the entire disposable income on the composite good without purchasing good X.
The slope of the budget constraint is determined by the price ratio of the two goods. In this case, it is -1/5 or -0.2. This slope indicates the rate at which the consumer can trade good X for the composite good. The budget line will start from the vertical intercept at 3,000 units of the composite good and end at the horizontal intercept at 600 units of good X, hence forming the budget constraint line.