Observations on equilibria

$P_x/P_y$ is the price ratio. Consider price ratio to be 1.

Also consider that $MU_x/MU_y$ be 1.

In this case, my exchange rate is the same as the exchange rate in the market.

If the slope indifference curve is the same as the slope of MRS, then there are multiple equilibria, given by the line of intersection of budget line and the IC.

Comparative static

What happens when parameters change?

Price change

Let $p_x$ decrease. This changes the budget line.

This causes an increase in the $x$ intercept. The $y$ intercept remains same. The slope changes.

This allows us to move towards a higher utility region in the utility map. The equilibrium point is shifted to a better position.

Note: the new equilibrium will have more of not only $x$, but also more of $y$.

Reason: when the price decreases, one's purchasing power increases. When the purchasing power increases, one tends to buy a lot of things.

Price and Income effects

Two effects in moving of equilibrium due to price change

1. Substitution effect (SE)

   Buy more of cheaper good. More of x, less of y.

2. Income effect (IE)

   Purchase more of both commodities, when one gets cheaper.

If SE > IE, less of y; and vice versa. This is determined by the utility map and the budget line.

Draw a line parallel to the final budget line, tangent to the initial IC. Call the intersection B. From initial equilibrium (A) to B is the substitution effect. From B to the final equilibrium point (C) is the income effect.

Income change

Only the budget line is affected. The slope remains same, but the intercept is changes.

The equilibrium point shifts to be more favorable, if the income increases.

Normal good and Inferior good

If income increases and consumer purchases more of a good, then the good is called a normal good. Most are normal goods.

Inferior goods are those that you purchase less when you have more income. Secondhand goods, cheap goods,