Saturday, August 27, 2011

Budget constraint


Shows the market baskets of goods and services a consumer can afford? Given the consumers income and the prices of goods and services in the baskets.

Px X +Py Y= I
  • I = consumers income
  • Px - price of good X.
  • Py - price of good Y
  • Qx - quantity of good X consumed.
  • Qy - quantity if good Y consumed.
Budget line.
A line showing all combinations of two goods that a consumer can afford if all income is spent over a period. Points in the budget line imply that the sum of all the expenditure on good X and Y must equal the consumer's income.


The horizontal and vertical intercepts measure how much the consumer should get if s/he spent all his/her money on goods 1 and 2 respectively X and Y. The slope of the budget line represents the amount of good Y obtained by giving up each unit of good X.

Changes in income and prices.

A change in income.
A change in income shifts the budget constraint outward (increase) or downward (decrease) parallel to itself.
An increase in income makes it possible for the consumer to purchase market baskets of goods and services that were previously unaffordable.

A change in the price of X.
Change in price of X rotates the budget line to a new intercept on the X-axis without changing the intercept of the Y-axis.

A change in the price of good Y. Change in Price of Y
Market Basket.
Let Px=$1.50; Py=$3.00 Also see table above.

Budget Line
If the consumer spent all of $15 on cassettes tapes, s/he can buy 5 cassettes during the week (B1) and s/he cannot purchase fuel.
Similarly B6 s/he spent all income on fuel Ю no cassettes.
B2 => PxQx + PyQy=I => $3 * 4 + $ 1.5 * 2 = $15
Similarly with all other baskets.

Market baskets represented by points above the budget line require more income per week that is currently unaffordable.

Foe example B7 consisting of 8 cassettes and 4 gallons of fuel per week would require a more income of $30 of which $24 will be needed for cassettes tapes and $6 for the fuel.
$3 * 8 + $1.5 * 4 = $30.

Market baskets below the budget line could be purchased without using up all of his/her weekly income
B8 = $3 * 1 + $1.5 * 4 = $9 => $15 - $9 = $6 is left.

We can use the equation for the budget constraint Px X +Py Y= I to find out how the maximum amount of each good that the consumer can purchase depends on the consumer income and the price of the good.

Let Qy=0 and so for Qx you'll get the maximum amount of good X the consumer can purchase over a period Thus from
Px X +Py Y= I
PxQx + Py (Qy =0) = I
Qx = I / Px --- the maximum amount of good X.

Similarly Qy = I / Py for maximum amount of good Y.

Change in Pr of X

Market baskets. Gallons of oil. Cassettes tape. Total expenditure.
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