Lecture 11 - Demand and Income Influencing Variables PDF

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Demand and Income Influencing Variables...

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Objective: Understand how regular demand depends on income, on prices Demand and Income Last time: how we can trace out the optimal consumption bundle at various income levels with the income expansion path. How to graph quantity demanded and Engel curves. Classification of goods and how they respond to income. Normal, inferior, luxury, necessities--categories of goods. Cobb Douglas demand, concluded that for such a consumer, all goods are normal and are neither luxuries or necessities, stay same to consumer regardless of the quantity. Perfect Complements We know that she will always consume at the consumption bundle with the kink in the indifference curve. Her income expansion path traces out the income expansion bundles with kinks in the curve. Because it is upwards sloping, all goods are normal. Neither luxury nor necessities because it is linear. Income expansion is a ray through the kinks in the indifference curves. Upwards sloping implies that all goods are normal. Linearity implies that the goods are neither luxury nor necessities. Makes the same choices regardless of how much of each quantity she has.

In this case, x1 is a luxury and x2 is a necessity. Luxury is strictly concave. Necessity is strictly convex.

In general, for a perfect complements good, this is the case.

Perfect Substitutes Demand She compares happiness per dollar for each good. This is independent of her income. For any given income, she will choose one of the two goods. As income increases, she chooses to consume the same good. Keep the prices the same, the steepness of the budget constraint does not change. Only corner solutions.

Income expansion path is a straight line, so the good that is consumed is a normal good. It is neither a luxury nor a necessity. Linear, upward sloping Engel curve.

The equation of the line.

All three consumers have consumption patterns that are income independent, mix the two goods regardless of the income that they have. Properties of preferences can be described as Homothetic Preferences Preferences are homothetic if the MRS depends on (x2/x1), but not on x1 and x2. Steepness of the indifference curves is allowed to depend on the relative mix of the quantities of the two goods but NOT on the absolute levels of the goods. Find the ideal consumption bundles in a ray from the origin, it can be described as the ratio of the quantities of the two goods. Along any ray from the origin, ratios are the same. Along any ray from the origin, the MRS must be the same. Cobb Douglas consumer has a marginal rate of substitution that is defined by (alpha/beta)*(x2/x1). Perfect Complements consumer. Indifference curves are either infinitely steep or infinitely horizontal. For a perfect substitutes consumer, indifference curves are linear and parallel. Quasi Linear Preferences are not homothetic. The indifference curves are oriented not towards the origin, but towards the horizontal axis. They are stacked vertically on top of each other. Consumption bundles where MRS is the same is found vertically on top.

Function is strictly increasing and concave.

Fixed relative proportion will cut along places where MRS is the same. MRS depends on the absolute levels of quantity of good one. This gives rise to dependence of consumption on income. Consumer will compare utility per dollar for each good then choose the good that gives her the best utility per dollar. Marginal utility of x1 is derivative of v function. Take first dollar and spend on x1. Income expansion path from the origin follows the x axis. She will initially spend all of her money on x1, when there is no x1 it is of the utmost importance. When she spends that dollar on x1, marginal utility will decrease. X1 is absolutely necessary if we don’t have any of it, as we accumulate more and more the marginal utility will fall. As we continue to give the consumer money, she continues to spend it on x1.

Income expansion path is initially horizontal along the x axis. At the first mark, her consumption changes. Not getting as much happiness as the potential. Marginal utility of x2 (constant) does not change. She will take the next dollar then spend it on x2. Marginal utility per dollar for x1 and x2 is still the same. Income expansion path becomes vertical. Income expansion path is heavily dependent on the income. Think of x2 as everything else in life she is interested in.

Allows for the idea that those who are poor will consume differently than the wealthy. X1 is a necessity and x2 is a luxury at income levels large enough that you will have an interior solution. The Engel curve is depicted below. In the diagonal income range, x1 is neither a necessity or luxury. Beyond that point, x1 becomes a necessity, importance in consumption begins to fall.

Nothing is lost in terms of economic intuition, as long as prices are strictly positive you won’t consume x1 beyond satiation point. Slope initially is the price of good 1. Change in behavior of consumer is what changes the slope. Relative importance of x1 begins to fall. The curve is strictly convex. The second Engel curve is strictly concave. Demand and the Price of the Good Itself Fix the price of x2 and the consumer’s income. Think of the quantity of x1 only as a function of its price. Changes in the optimal consumption bundle. Consumer chooses an optimal consumption bundle along the indifference curve. Budget constraint swings out on the x axis. Now consumer will then find a new consumption bundle along the new budget constraint. Price

offer curve is created by fixing income and price of other goods. Decrease the price of x1 from infinity, this gives me vertical budget constraint, until price of x1 becomes zero it will be perfectly horizontal. For infinite number of budget constraints, note where optimal consumption bundles are. As the price of x1 falls, it traces out where consumer has optimal consumption bundles.

Graph of x1 as a function of its price. Vertical axis is independent, horizontal axis is dependent. We graph the inverse demand. Think of the price as a function of the good itself (Marshallian demand). Inverse demand curve--for any quantity of x1 it will tell us what the price must have been for the selected quantity. Inverse demand is the consumer’s valuation (in money) of x1.

Tangency condition implies that price of x1 must be equal to MRS * p2. MRS tells us the consumer’s valuation of unit of x1 in terms of units of x2 that she thinks it is worth....