ECON 300

When is the budget constraint not binding?

If the assumption of monotony fails

What is the budget constraint formula?

PxX + PyY = m

When does an interior solution take place?

When both goods are being consumed. If x is very small, meaning the marginal utility of an additional unit is high, meaning you are willing to spend income, then the marginal utility will be close to infinity. So, when limit as x goes to 0 of the Marginal Utility of x and y is infinity, we have an interior solution.

When does a corner solution take place?

When you are consuming only one good

What are the steps if the interior solution conditions work?

If the preferences are monotone, you can use the lagrangian method. Otherwise, you can solve the system of equations: MRS = px/py, budget constraints for x and y.

What are the steps if the interior solution condition does not hold?

Use normal steps to find the interior solution, and then calculate the utility from that bundle. You then find corner solution quantities and determine their utility: in the budget constraint, set one variable to 0 and solve for both. Whichever produces the highest utility will be the optimal bundle.

What are the conditions for a lagrangian?

Monoticity, and the sufficient condition for an interior solution.

What are monotonocity?

Ceteris paribus, a consumer always prefers more of a good to less of a good.

What is the lagrangian method?

Calculate Marginal utiltity. If it is greater than 0, preferences are monotionic. Check that limit of x going to 0 equals infinity. Set up the lagrange, take three first order conditions, set all equal to 0. Rearrange first two equations so they equal lagrange. Set them equal to each other which also ends up being the MRS. Solve for one variable and place it in the budget constraint/FOC 3. Plug that variable back into FOC 3 to solve for the other one. Now you have marshallian demand functions, which you can put the prices given into.

What are marshallian demand functions?

X and Y in what you end up with after the lagrange with the variables still in them.

Is interior utility function positive or negative?

Positive

How do you solve by utility maximization for functions that are monotone but not convex?

The equation is U(x+y) = x+y. Do the maximization constraint problem px + py < = m. Once you take a partial derivative, there is no x or y, so you reqrite to a tangency condition. MRS = MUx/MUy = Px/Py. Then solve for demand when MUx/Px = MUy/y. Solve the function for marginal utility. (edit this flashcard)

What are leontif preferences for, and give the equation?

Perfect complements - U(x,y) = min[x,y]

Are leontif utility functions differentiable?

Not necessarily at the point where they intersect

What is true about the marginal utility of x in Leontif preferences?

If x < y, then u(x,y) = min [x,y] = x. The marginal utility of x is 1, and the marginal utility of y is 0, and is vertical. If x is greater than or equal to y, then u(x,y) = min[x,y] and

How do you solve Leontif preferences?

Using the budget constraint, set y = x. You then substitute each variable into the budget constraint to solve for y and x.

What is the general solution for Leontief preferences?

x = m/px + py, y = m/px + py. m is the numerator and the prices of sums are in the denominator.

When is the curve convex?

x rises and MRS falls, so it is diminishing

When is the curve concave

x rises and MRS rises

What is the revealed preference approach?

An approach to determining consumer preferences by predicting preferences from their choices. If both choices are available and the consumer chooses one, that is their preference.

What happens to the budget line when price changes?

Whatever good the price has changed of, it will rotate around the intercept of that good.

What is a price consumption curve?

Connects all the utility maximization points (where budget line intersects with indifference curve) on a given indifference curve graph.

What is the relationship of price and demand in substitutes?

Increase in one good prices, increase in quantity demanded of the other, or a decrease in the price of one leads to a decrease in the quantity demanded of the other.

What is the relationship of the properties of price and demand in complements?

An increase in the price of one leads to a decrease in the quantity demanded of the other. A decrease in the price of one leads to an increase in the quantity demanded of the other.

What happens to the demand curve when substitute prices increase?

Right shift

What happens to demand curves when complement prices decrease?

Right shift

What happens to demand curve when substitute prices decrease?

Left shift

What happens to demand curve when complement prices increase?

Left shift

What is the income consumption curve?

Joins all the optimal points on income curves.

What is the engel curve?

When the prices is fixed but income changes, demand curves shift. The optimal points in those cases are the engel curve.

What are some properties of a normal good?

ICC has a positive slope, quantity demanded increases with income, indicating income elasticity of demand is positive

What are some properties of an inferior good?

Quantity demanded decreases with income, income elasticity of demand is negative, income consumption curve has a negative slope.

What are properties of luxury goods?

Income elasticity of demand is greater than 1, quantity demanded increases more than proportionally with income

What are the properties of necessities?

Income elasticity is between 0 and 1, quantity demanded is less than proportional with income