Question

properties of budget line?

Answer 1

i) Since budget line is derived from a linear budget equation M = XPx + YPy, so it is a straight line. The intercepts of this line with the axes show the maximum amount of one commodity that can be purchased, if none of the other is bought.

(ii) Budget line has a negative slope, i.e., slopes downward from left to right. The negative slope of the budget line is mathematically established by noticing coefficient of ‘X’, i.e., – PX/PY when the budget equation is rearranged (see pictures)
iii) Mathematically, the slope of the budget line is derivative ∂Y/∂X or coefficient of ‘X’ in the above equation. Thus, the slope of the budget line is negative of the price ratio, i.e., – Px/ Py. If prices of commodity ‘X’ and commodity ‘Y’ are equal, then, the budget line would have a 45° angle with both the axis.
iv) So long as the price ratio remains the same, the slope of the budget line will be the same. If for the same budget for the consumer, prices of both the commodities rise and fall by the same proportion, the budget line will have an outward and inward parallel shift in the two cases respectively
(vi) Budget line depicts the boundary line (or dividing line), below which lies the region containing attainable combinations of the two commodities. This right angled triangle formed between the budget line and the axes is called the feasible consumption choice set or budget set 
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Answer 2

1. It will be a straight line 
2. It will be downward sloping or will have a negative slope.
3. The slope of the budget line will be equal to the negative inverse of the ratio of the prices i.e.
4. Budget line can shift inwards and outwards with the change in income and no change in the prices of the good.