Managerial Economics Midterm #1

What is the formula for the present value (PV) of a payment?

PV = Payment / (1+i)^t

What is an explicit cost?

A direct out-of-pocket expense (e.g., tuition, fees).

What is an implicit cost?

The opportunity cost of lost income or benefits (e.g., wages not earned while in school).

What is Net Present Value (NPV)?

NPV = PV(benefits) − PV(costs)
Decision Rule: Invest if NPV > 0.

How do you calculate PV of an annuity that pays forever?

PV = Annual Cash Flow​ / i

Decision rule for comparing projects with different NPVs?

Choose the project with the higher NPV.

What is the formula for the present value of a firm with growing profits?

PV = π₀​(1+i)​ / i - g

(where π0\pi_0π0​ = initial profit, iii = interest rate, ggg = growth rate.

What happens to firm value if the interest rate increases?

Value decreases because future profits are discounted more heavily (higher opportunity cost of waiting).

What is the effect of a higher growth rate g on firm value?

Value increases (future profits grow faster)

General form of demand function in your assignments?

Q_x^d​ = 20 − P_x ​− 2P_y ​+ 3M

How do you find the inverse demand curve?

Solve for P_x in terms of Q_x​:

P_x = constant − Q_x​

The constant changes if P_y or M changes.

What does a decrease in P_y do to demand for X?

Shifts the demand curve outward (higher constant in the inverse demand equation).

Formula for elasticity of demand with respect to variable Z?

E_Q,_Z = ∂Q / ∂Z = Z / Q

How to interpret own-price elasticity?

• If |E| > 1 → elastic (sensitive to price).

• If |E| < 1 → inelastic (not very sensitive).

• Always negative for downward-sloping demand.

How to interpret cross-price elasticity?

• Positive → substitutes (price of Y ↑ → demand for X ↑).

• Negative → complements (price of Y ↑ → demand for X ↓).

How to interpret income elasticity?

• Positive → normal good.

• Negative → inferior good.

Formula for % change in quantity demanded given elasticity?

%ΔQ = E_Q,_P ⋅ %ΔP

How do you calculate the change in revenue when price changes?

ΔR = [R_c​(1 + E_{Qc​,Pc​​})+R_t​(E_{Qt​,Pc​​})]⋅%ΔP_c​

(where R_c = revenue from coffee, R_t = revenue from tea)

How do you know if raising price increases total revenue?

If demand is inelastic (|E| < 1), revenue ↑.
If elastic (|E| > 1), revenue ↓.

How do you tell if goods X and Y are substitutes or complements from a log-linear demand function?

Look at the sign of the coefficient on ln⁡P_y​:

• Positive → substitutes.

• Negative → complements.

How do you determine whether X is a normal or inferior good from a log-linear demand function?

Look at the coefficient on ln⁡M (income elasticity):

• Positive → normal good.

• Negative → inferior good.