A Few Applications of Review Material Budget Constraints Isocosts Utility Functions Production Functions

Deriving the Budget Constraint  A consumer consumes goods X and Y, which have prices P x and P y with income I  Expenditures are: P x X + P y Y  Along the budget constraint, all income is spent: P x X + P y Y = I

Budget Constraint algebra Intercept:Slope:

Budget Constraint X Y Not affordable Affordable I/P x I/P y Slope = -P x /P Y The affordable bundles are together known at the Opportunity Set or Budget Set

Budget Constraint for Three Commodities x2x2 x1x1 x3x3 I /p 2 I /p 1 I/p 3 p 1 x 1 + p 2 x 2 + p 3 x 3 = I This is a plane instead of a line.

Change in income: pay raise X Y

Change in price: X gets cheap X Y

Example: The Food Stamp Program  Consider the two good example where consumers purchase food (F) and all other goods are lumped into one category (G).  Suppose I = $100, p F = $1 and the price of “other goods” is p G = $1.  The budget constraint is then F + G =100.

Example: The Food Stamp Program G F 100 F + G = 100: before stamps.

Example: The Food Stamp Program  Now assume that the government offers each family food stamps worth $40.  Draw the new budget constraint of a typical family.

Example: The Food Stamp Program G F 100 Budget set after 40 food stamps issued. 140 The family’s budget set is enlarged. 40