Final answer:
The equation for the budget line is 8x1 + 4x2 = 40. The budget line can be drawn in (x1, x2) space by rearranging the equation to solve for x2 and plotting different values of x1. If all of your money is spent on good 1 or good 2, you can afford 5 units of good 1 or 10 units of good 2 respectively. The rate at which you can trade good 1 for good 2 and remain on the budget line is 2:1. If there is a tax of $2 on each unit of good 1 consumed, the new budget line equation becomes 10x1 + 4x2 = 40.
Step-by-step explanation:
a. The equation for the budget line can be written as follows:
p1x1 + p2x2 = income
where p1 and p2 are the prices of goods 1 and 2 respectively, x1 and x2 are the quantities of goods 1 and 2 consumed, and income is the consumer's income. In this case, the equation becomes 8x1 + 4x2 = 40.
b. To draw the budget line in (x1, x2) space, we can rearrange the equation to solve for x2: x2 = (40 - 8x1) / 4. We can then plot different values of x1 on the x-axis and calculate the corresponding values of x2 using the equation. The resulting line represents the budget line.
c. If you spend all of your money on good 1, the equation becomes 8x1 = 40, which gives x1 = 5. So you can afford 5 units of good 1 if you spend all of your money on it.
d. Similarly, if you spend all of your money on good 2, the equation becomes 4x2 = 40, which gives x2 = 10. So you can afford 10 units of good 2 if you spend all of your money on it.
e. The rate at which you can trade good 1 for good 2 and still remain on the budget line is given by the ratio of their prices. In this case, the ratio is 8/4 = 2, which means you can trade 2 units of good 1 for 1 unit of good 2 and still remain on the budget line.
f. If there is a tax of $2 on each unit of good 1 consumed, the new price of good 1 would be $10 (8 + 2). The new budget line equation becomes 10x1 + 4x2 = 40.