Question

Show consumer's equilibrium with the help of indifference curve.

Hint:

Consumer equilibrium occurs where the budget line is tangent to an indifference curve, indicating that the marginal rate of substitution equals the price ratio.

Answer 1

Consumer equilibrium refers to the point at which a consumer reaches the maximum possible satisfaction, given their budget constraint and preferences for different goods. This is achieved when the consumer allocates their income between goods in a way that maximizes utility.
Step 1: Indifference Curve Analysis.
In indifference curve analysis, consumer equilibrium is achieved at the point where the budget line (representing the consumer’s income and the prices of goods) is tangent to an indifference curve. This means that the consumer is obtaining the highest level of satisfaction (utility) from the consumption of two goods within their budget.

Step 2: Budget Line.
A budget line represents all possible combinations of two goods that a consumer can afford, given their income and the prices of the goods. The slope of the budget line is determined by the relative prices of the two goods.

Step 3: Tangency Condition.
At the point of consumer equilibrium, the budget line is tangent to an indifference curve. This tangency point occurs when the marginal rate of substitution (MRS) between the two goods is equal to the ratio of their prices. Mathematically, this is expressed as: \[ MRS = \frac{P_x}{P_y} \] Where \( P_x \) and \( P_y \) are the prices of the two goods. At this point, the consumer cannot increase satisfaction by shifting consumption between the two goods.

Step 4: Consumer’s Equilibrium.
At the equilibrium point, the consumer maximizes their satisfaction, given their income and the prices of the goods. The consumer will allocate their income such that the marginal utility per dollar spent on each good is equal, ensuring optimal consumption.
Step 5: Graphical Representation.
The equilibrium is represented graphically as the point where the budget line is tangent to the highest possible indifference curve. The slope of the budget line equals the slope of the indifference curve at this point.