Question

2) When an agent maximizes utility given a certain budget, how can we solve the problem graphically? Show a general case for ‘Cobb-Douglas preferences’. (In other words, what is the condition that has to be met between budget line and indifference curve in order to maximize an individual’s utility?)

Answer 1

* A rational consumer will be in equilibrium when his utility is maximized within budget constraint. At optimal choice slope of indifference curve i.e. MRS (Marginal rate of substitution) will be equal to slope of budget line i.e. P1 / P2 . There equality is required bacause MRS measures the rate at which consumer is willing to exchange one good for the other while price ratio measures the rate at which consumer can exchange one good for the other in the market.

Therefore, If these two ratios are not equal then consumer will change the consumption bundle. For example -:
1) If MRS > P1 / P2 then consumer will purchase more of good 1 and less of good 2.
2) If MRS < P1 / P2 then consumer will purchase more of good 2 and less of good 1

* For the Cobb-Douglas preference the optimal consumtion is bundle is shown in the below diagram. The optimal choice occurs where MRS = P1 / P2 .