Final answer:
Jon's budget constraint equation is 20X + 10Y = 200. He can afford a maximum of 10 units of good X or 20 units of good Y. His optimal consumption bundle of good X and good Y is indifferent along the budget line because X and Y are perfect substitutes and provide equal utility per dollar.
Step-by-step explanation:
When considering Jon's budget constraint, we must look at his income and the prices of goods X and Y. Since good X costs $20 and good Y costs $10, and Jon has $200 to spend, his budget constraint equation can be expressed as 20X + 10Y = 200. The maximum quantity of good X Jon can afford is 10 (200/20), and the maximum quantity of good Y he can afford is 20 (200/10).
To draw the budget constraint, you place the quantity of good X on the horizontal axis and the quantity of good Y on the vertical axis. The budget line would intersect the axes at the points mentioned above (10, 0) for good X and (0, 20) for good Y. The slope of this line would be -2, indicating the rate at which Jon can trade good Y for good X.
Given that X and Y are perfect substitutes and Jon's Utility function is U(X, Y) = X + Y, Jon will maximize his utility by spending his entire budget on the good that provides the most utility per dollar. Since both goods provide equal utility per dollar (as indicated by the utility function), Jon will be indifferent to any combination of X and Y along the budget constraint. Therefore, his optimal consumption bundle could be anywhere along the budget line.