Question

Suppose a consumer has an income of birr 800 per month and he wants to spend all of his income on two goods apple and orange whose prices are 8 and 10 birr respectively . Based on this information answer the following questions. A.express the budget line of the consumer both algebrically and diagramatically. B.compute the equation of the budget line C.determine the slope of the budget line and interpret the result D.what will happen to the origional budget line? 1.if money income doublees. 2.if the price levels increases by 50 percent. 3.if price of orange doubles.

Answer 1

a) Given the prices of two goods, and denoting quantity of goods apples and oranges by A and O, respectively. Then, budget line can be written as:

Price of apple$\times$ quantity of apples + price of orange$\times$ quantity of oranges = income

$8\times A + 10\times O = 800$

Graphically, this can be seen as:

oranges on dependent (Y) axis and apples on independent (X) axis, we can write the required budget line equation as:

$O =\frac{ (800 - 8A)}{10}\\ O = 80 - 0.8\times A$

b) $8 A + 10O = 800$

c) Slope of the budget line is then 0.8

Interpretation: as quantity of apples increase by a unit, for oranges it decreases by 0.8

d) 1. If income doubles: new budget line can be written as $8\times A + 10\times O = 2\times 800$

$8A + 10O = 1600,$ so budget line can be shifted outwards parallelly (doubling the consumption set).

2. If price levels increase by 50%, new budget line:$(1+50\%)\times 8\times A + (1+50\%)\times10 = 800$

$8A + 10O = \frac{800}{(1+50\%)}\\ 8A + 10O = 0.667\times 800$

So, the budget line would shift inward, this is similar to reduction in income by 33.33%

3. If price of orange doubles (which is same like increase by 100%), new budget line is:

$8A + 2\times 10O = 800\\ 8A + 20O = 800,$ which changes the slope of budget line (new slope $= \frac{8}{20} = 0.4$ , which is lower, so flatter budget line), new budget line is pivoted inward around the intercept of apples line.