Question

Define Optimization in an indifference curve along with relevant examples?

Answer 1

 

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Step 2

Optimization involves maximizing the utility of consumer, subject to the budget constraint. The budget constraint shows the bundles that the consumer can afford, given his income level and prices.

Optimizations allows the consumer to reach the highest indifference curve for a certain income level. At this point, the consumer attains maximum possible satisfaction and can't be made any better off.

For example, consider two goods X and Y. The utility function is given as: 

U = XY.PX = 1, PY = 3. Income (M) = 200.">U = XY.PX = 1, PY = 3. Income (M) = 200.U = XY.PX = 1, PY = 3. Income (M) = 200.

Now, for optimization, we have:

max U = XY,st. PX.X + PY.Y = M (budget constraint)">max U = XY,st. PX.X + PY.Y = M (budget constraint)max U = XY,st. PX.X + PY.Y = M (budget constraint)

This occurs where slope of indifference curve equals the slope of budget line.

Slope of indifference curve = MUXMUY = YX">Slope of indifference curve = MUXMUY/ = YX/Slope of indifference curve = MUXMUY = YX.

Slope of budget line = PXPY = 13.">Slope of budget line = PXPY/ = 13./Slope of budget line = PXPY = 13.

Equating the two, we solve for X in terms of Y and then substitute it in the budget constraint. This resultant solution provides the optimal solution for X and Y.

Step 1

An indifference curve shows various combinations of two goods that give same level of utility to a consumer. This means that a consumer remains indifferent along an indifference curve.

Usually, an indifference curve is downward sloping. A higher indifference curve indicates higher utility.