Question 1. Consider a consumer allocating a budget of $100.00 between two goods, X and Y. The price of X is $10.00 per unit and the price of Y is $5.00 per unit.
(a) in a diagram show how the consumer's budget constraint will be affected if the consumer's budget rises to $300.00 while the price of Y doubles and the price of X remains unchanged.
(b) With the aid of indifference curves show how the above changes might affect the consumption of X.
Comment: The simplest way to draw a budget constraint line is simply by calculating the maximum number of units that can be bought of either of the two goods (if nothing is bought of the other one) and then connecting these quantities with a straight line.
Consider: if I=100 and Px = 100/10=10 units of X.
and if I=100 and Px=5 then you could buy I/Px=100/5=20 units of Y.
The resulting graph of the budget constraint will then look as follows
Next the income rises to 300 while Px=10 and Py=10 so now you could buy at most 30 units of either good.
As for part b, you are not provided a formula for calculating an indifference curve. So this is not about a precise answer, but rather about showing that for either of these budget constraints, you would expect the utility to be maximized at a point of tangency. Where the tangency point is will depend on exactly how you draw the relevant indifference curves. In the following diagram the quantity of X changes from 10 to 14, but this is just an example and its perfectly fine if your diagram shows different changes in x as long as these are based on properly drawn indifference curves.