intermediate micro 1

Marginal utility

The extra satisfaction from getting a little more of one good.

Indifference curve

All the bundles of two goods that make the consumer equally happy. Curves further from the origin mean higher utility.

Marginal rate of substitution (MRS)

How much of one good the consumer is willing to give up to get a bit more of the other and stay equally happy. It is the slope of the indifference curve.

Budget constraint

All the bundles the consumer can afford with their income. Its slope shows the market trade-off between the two goods (the price ratio).

What is true at the consumer's optimum?

The consumer's willingness to trade (MRS) equals the market trade-off (price ratio). Graphically: the indifference curve just touches the budget line.

Corner solution

The consumer spends everything on one good and buys none of the other. The tangency rule doesn't hold because the consumer can't buy negative amounts.

Perfect complements

Goods that are only useful together in fixed proportions (left and right shoes). Indifference curves are L-shaped.

Perfect substitutes

Goods the consumer treats as interchangeable at a constant rate. Indifference curves are straight lines.

Why do we skip Lagrange multipliers in this course?

Your professor said to ignore them. We solve by substituting the budget constraint into the utility function instead.

Price-consumption curve

Shows how the consumer's best bundle changes as one price changes (income and the other price stay fixed).

Income-consumption curve

Shows how the consumer's best bundle changes as income changes (prices stay fixed).

Engel curve

A graph of how much of a good the consumer buys as income rises.

Substitution effect

When a good gets cheaper, the consumer switches toward it because it is relatively cheaper than the other good. Think: same happiness level, different mix. It always pushes you to buy more of the good whose price fell.

Income effect

When a price falls, the consumer's purchasing power rises, so they feel richer and buy more of normal goods. Think: a price drop is like getting a raise.

Total (net) effect of a price change

Substitution effect + income effect. For a normal good the two effects point the same way, so a price fall clearly increases quantity. For the OTHER good the effects pull in opposite directions, so the net sign is unclear.

Normal good

A good you buy more of when income rises.

Inferior good

A good you buy less of when income rises (you trade up to something better).

Necessity vs luxury

Both are normal goods. Necessity: spending grows less than proportionally with income. Luxury: spending grows more than proportionally with income.

Ordinary (Marshallian) demand vs compensated demand

Ordinary demand: price changes and you feel both effects (income left unchanged). Compensated demand: you are given or taken enough income to keep you at the SAME utility, so only the substitution effect shows up.

Why is the compensated demand curve steeper than the ordinary demand curve (for a normal good)?

Because it removes the income effect, so the quantity response to a price change is smaller.

Slutsky equation (in words)

Total effect of a price change = substitution effect + income effect. It lets you split any demand response into those two parts.

Indirect utility

The highest utility the consumer can reach given prices and income.

Expenditure function

The least money needed to reach a given utility level at given prices. It is the mirror image of utility maximization.

Shephard's lemma (in words)

How much the minimum expenditure rises when a price goes up = the amount of that good you were buying (compensated demand).

Compensating variation (CV)

How much money you would need to be given after a price rise to get back to your ORIGINAL happiness level. Measures the welfare loss using the old utility.

Equivalent variation (EV)

How much money you would give up BEFORE the price rise to be as badly off as you would be after it. Measures the welfare loss using the new, lower utility.

CV vs EV vs change in consumer surplus

For a price increase, CV is the biggest and EV the smallest. The change in consumer surplus (area under the ordinary demand curve) falls in between, so it is a handy compromise that needs no utility theory.

Consumer surplus

The gap between what consumers are willing to pay and what they actually pay. Shown as the area under the demand curve and above the price.

Market demand

Add up everyone's individual demand at each price. It depends only on total income if everyone has the same preferences; otherwise it also depends on who has the income.

Elasticity

How much one thing changes in percentage terms when another rises by 1%.

Own-price elasticity of demand

How much quantity demanded changes (in %) when the good's own price rises 1%. Usually negative.

Elastic, unit elastic, inelastic demand

Elastic: quantity is very sensitive to price (beyond -1 in size). Unit elastic: exactly proportional. Inelastic: quantity barely reacts to price.

Income elasticity of demand

How much quantity demanded changes (in %) when income rises 1%. Negative = inferior, between 0 and 1 = necessity, above 1 = luxury.

Cross-price elasticity of demand

How much demand for good 1 changes when the price of good 2 changes. Positive for substitutes, negative for complements (though the sign can be ambiguous in theory).

Does elasticity stay constant along a straight-line demand curve?

No. It changes along the curve: demand is more elastic at high prices and less elastic at low prices.

Constant-elasticity demand curve

A demand curve shaped so that the same percentage price change gives the same percentage quantity change at every price.

Shift of the demand curve vs movement along it

A change in the good's own price moves you ALONG the curve. A change in income, in other goods' prices, or in tastes SHIFTS the whole curve.

What happens to demand for good 1 if the price of a complement rises?

Demand for good 1 shifts in (falls), because the pair gets more expensive to use together.

What happens to demand for good 1 if the price of a substitute rises?

Demand for good 1 shifts out (rises), because consumers switch toward it.

What happens to market demand when consumers get richer?

For a normal good, it shifts out. For an inferior good, it shifts in.

Production function

The recipe that turns inputs (capital, labor, materials, land) into output.

Capital and labor prices

Capital is rented at rate r and labor is hired at wage w. The firm takes both as given.

Marginal product

The extra output from adding a little more of one input while holding the other inputs fixed.

Average product of labor

Output per worker (labor productivity).

When is total output at its maximum (with one input)?

When the marginal product of that input hits zero: one more unit adds nothing.

How are marginal product and average product related?

If the marginal product is above the average, adding labor pulls the average up. If it is below, adding labor pulls the average down. So they cross at the peak of the average.

Diminishing marginal product

Eventually, each extra unit of an input adds less output than the one before, if the other inputs stay fixed.

Isoquant

All the combinations of capital and labor that produce the same output. It is the firm's version of an indifference curve.

Properties of isoquants

They don't cross, don't slope upward, and higher ones mean more output. They are usually bowed in (convex).

Marginal rate of technical substitution (MRTS)

How much capital the firm can give up if it adds one more unit of labor and still produces the same output. It is the slope of the isoquant.

Diminishing MRTS

The more labor the firm already uses, the less capital it can give up for each extra worker. This is why isoquants are convex.

What does MRTS equal in terms of marginal products?

The ratio of the marginal products: MP of labor divided by MP of capital.

Elasticity of substitution

How easily a firm can swap one input for another as their relative importance changes. High: inputs are close substitutes and the isoquant is fairly flat. Low: the inputs must be used together and the isoquant is sharply bent.

Perfect complements vs Cobb-Douglas vs perfect substitutes (production)

Perfect complements (Leontief): inputs used in fixed proportions, L-shaped isoquant, no substitution. Cobb-Douglas: moderate substitution. Perfect substitutes: straight-line isoquant, inputs fully interchangeable.

Constant returns to scale (CRS)

Double all inputs and output exactly doubles.

Decreasing returns to scale (DRS)

Double all inputs and output less than doubles (e.g. a huge firm is hard to manage).

Increasing returns to scale (IRS)

Double all inputs and output more than doubles (e.g. workers specialize).

Returns to scale vs diminishing marginal product

Returns to scale: change ALL inputs together. Diminishing marginal product: change ONE input and hold the others fixed. They are different ideas.

Why is CRS convenient?

The MRTS depends only on the capital-labor ratio, not on the output level. So the isoquants look alike along any ray from the origin.

Technological progress

The firm can make the same output with fewer inputs, which shifts the isoquant inward.

Hicks-neutral technological progress

The isoquant shifts in without changing shape, so the best capital-labor mix at given input prices doesn't change.

Labor-saving vs capital-saving technological progress

They change the SHAPE of the isoquant. Labor-saving: the improvement makes capital more productive, so the firm becomes capital-intensive. Capital-saving: the improvement makes labor more productive, so the firm becomes labor-intensive.

Perfect competition in factor markets

Each firm is so small that it can buy as much capital and labor as it wants at the going prices without moving them.

Isocost line

All the combinations of capital and labor that cost the same total amount. Its slope shows how the market trades off capital for labor (the input price ratio).

Cost minimization (the key idea)

Produce a target output at the lowest cost: pick the point where the isoquant just touches the lowest possible isocost line. There, the firm's technical trade-off (MRTS) equals the market trade-off (input price ratio).

Expansion path

The line connecting the cost-minimizing input bundles as the firm's output target rises, with input prices held fixed.

Why is cost linear in output under CRS?

Doubling output requires exactly doubling every input, and so exactly doubling cost.

Total, average, and marginal cost

Total cost: everything the firm pays. Average cost: total cost per unit. Marginal cost: the extra cost of producing one more unit.

Average and marginal cost under CRS

Both are the same constant number, so they are flat horizontal lines.

U-shaped average cost

Average cost falls at low output (increasing returns), bottoms out at the efficient scale (constant returns), then rises (decreasing returns).

How do marginal cost and average cost relate?

If marginal cost is below average cost, average cost is falling. If it is above, average cost is rising. So marginal cost crosses average cost at the minimum of average cost.

Short run vs long run

Short run: at least one input (capital) is fixed. Long run: the firm can change all inputs.

Fixed cost vs variable cost

Fixed cost: paid no matter how much the firm produces (even zero). Variable cost: changes with output.

Average fixed cost, average variable cost, short-run average cost

Short-run average cost = average fixed cost + average variable cost. Average fixed cost keeps shrinking as output grows, so average variable cost gets closer to short-run average cost at high output.

Why is cost minimization 'meaningless' in the short run?

Capital is fixed, so the firm has no choice about its input mix. It just hires the labor needed for the output it wants.

Why is short-run cost never lower than long-run cost?

In the long run the firm can pick the best capital level; in the short run it is stuck with whatever capital it has, so it may be using the wrong mix.

When are short-run and long-run cost equal?

Only at the output level where the fixed capital happens to be the best choice.

Long-run average cost vs short-run average cost curves

Each level of fixed capital gives its own short-run curve. The long-run average cost curve touches each one at a single point and lies below the rest, tracing out their envelope.

Competitive firm's short-run supply curve

The part of the marginal cost curve above the shutdown price. The firm produces where price equals marginal cost.

Shutdown price

The price below which the firm shuts down in the short run: when price is less than minimum average VARIABLE cost, it can't even cover its variable costs.

Price at which a firm just breaks even

Minimum average (total) cost. Below it the firm loses money; it may still operate in the short run if price covers variable cost.

Short-run producer surplus

Revenue minus variable cost; the area between the price and the marginal cost (supply) curve. It also equals profit plus fixed cost.