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• Study notes for Microeconomics Midterm 1

Budget, Utility, Consumer Choice (Chapter 3)

• Budget constraint equation: ( p_x x + p_y y = I )
• ( \frac{p_x}{p_y} ) quantifies the tradeoff between goods x and y based on their prices
• A change in the price of either good ( p_x ) or ( p_y ) alters the budget line
• A change in income/budget ( I ) also affects the budget line
• Multiple simultaneous shocks in ( p_x ), ( p_y ), and/or ( I ) can cause budgets to shift and change slope concurrently

Preference

• Indifference curve
• Marginal utilities (MU)

Computation of Marginal Utilities

• For a linear utility function (perfect substitutes), marginal utilities can be computed

Marginal Rate of Substitution (MRS)

• ( MRS = \frac{\Delta y}{\Delta x} = \frac{MU_x}{MU_y} )
• Diminishing MRS and diminishing MUs exist

Consumer Choice (Utility Maximization Problem)

• Two conditions for optimal consumer choice: the budget condition must bind, and tangency
• Budget condition equation: ( p_x x + p_y y = I )
• Tangency condition: ( MRS = \frac{p_x}{p_y} )

Evaluate the optimality of a bundle on the budget:

• By comparing ( \frac{MU_x}{MU_y} ) vs ( \frac{p_x}{p_y} )
• If ( \frac{MU_x}{p_x} ) vs ( \frac{MU_y}{p_y} ) are not equal, determine if the indifference curve is steeper or flatter than the budget line
• Solving for consumer choice involves finding optimal ( x^* ) and ( y^* )
• Special cases include: Cobb-Douglas, perfect complements, perfect substitutes

Demand (Chapter 4)

• The demand curve can be derived graphically from the consumer choice problem
• Special cases of demand curves include: perfect substitutes, perfect complements, Cobb-Douglas

Effects on Consumer Choice x(px)

• Examines effects of income, own-price, and cross-price on consumer choice ( x(p_x) )
• Effect of (own) price results in movement along the demand curve
• Effect of income
  • Two types of goods: Normal goods vs. inferior goods
  • Income acts as a demand shifter
• Effect of cross-price
  • Two types of relations between goods: Substitutes vs. complements
  • Other goods' prices act as demand shifters

Movements Along the Demand Curve

• All else equal, the consumption ( x ) changes as the consumer reoptimizes when the good's own price ( p_x ) varies

Shifts of the Demand Curve

• All else equal, the consumption ( x ) changes as the consumer reoptimizes when other factors (consumer's own preference, income, another good's price) changes
• Demand can shift left or right depending on the shocks

Elasticity

• (Own-price) elasticity of demand: ( e^d = \frac{\Delta Q%}{\Delta P%} )
• Project percentage changes in consumption following a price shock
  • Computing ( \Delta Q% ) following some ( \Delta P% )
• Project percentage changes in expenditure/revenue, following a price shock
  • Computing ( \Delta (PQ)% ) following some ( \Delta P% )
• Calculate the elasticity for a linear demand
  • Using ( e = \frac{\Delta Q%}{\Delta P%} = \frac{\Delta Q}{\Delta P} \cdot \frac{P}{Q} )

Income Elasticity

• Income elasticity: ( e^I = \frac{\Delta Q%}{\Delta I%} )
• Income elasticity for normal, luxury, necessity, and inferior goods
• Project percentage changes in consumption and expenditure following an income shock
  • Computing ( \Delta Q% ) and ( \Delta (PQ)% ) following some ( \Delta I% )

Cross-Price Elasticity

• When symmetric, the cross-price elasticity between ( x ) and ( y ) is ( e_{x,y} = e_{y,x} )
• ( e_{x,y} = \frac{\Delta Q_y %}{\Delta P_x %} = \frac{\Delta Q_x %}{\Delta P_y %} )
• Project percentage changes in consumption and expenditure, following a price shock of another good
  • Computing ( \Delta Q% ) and ( \Delta (PQ)% ) following some ( \Delta P% ) of another good

Decomposition of Own-Price Effect

• Decompose own-price effect into: substitution effect + income effect
• Direction of these two effects:
  • Substitution effect: always the same as the law of demand
  • Income effect: can be either, depending on normal/inferior goods
• Magnitude of these two effects:
  • Substitution effect: depending on substitutable goods in the market
  • Income effect: depending on the income elasticity
• Applications: Explain/speculate why the price elasticity is relatively high/low for some goods by analyzing:
  • The size of the substitution effect
  • The direction and size of the income effect
• Substitution Bias from CPI
• Lump-sum tax & subsidy vs. per-unit tax and subsidy

Production, Isoquant, and MRTS (Part of Chapter 7)

• Production basics:
  • Total product (TP); MP and AP of an input (e.g., ( MP_L ) and ( AP_L ))
  • AP vs MP: AP increases when ( MP > AP ), and falls when ( MP < AP )
  • TP vs MP: TP increases when ( MP > 0 ), and falls when ( MP < 0 )
  • Compute MP and AP
  • Diminishing MP
• Isoquant for the production of 2 inputs
  • Production function ( F(L, K) )
  • Isoquant at a certain quantity ( Q_0 ), i.e., input combos such that ( F(L, K) = Q_0 )
  • A higher isoquant curve means more production with the same combinations of inputs

MRTS and Productivity Tradeoff

• Understand and calculate Marginal Product, e.g., ( MP_L ) and ( MP_K ) ( MRTS = \frac{\Delta \text{Input2}}{\Delta \text{Input1}} ), e.g., for ( L ) and ( K ), ( MRTS = \frac{\Delta K}{\Delta L} )

• ( MRTS = \frac{MP_1}{MP_2} ), where ( MP_1 ) is the marginal product of the first input on the x-axis and ( MP_2 ) is the marginal product of the second input on the y-axis

  • E.g., for L and K, ( MRTS = \frac{MP_L}{MP_K} )

• Diminishing MRTS (and sometimes diminishing MPs)