Formulas

Question 2

What is the two-step procedure to derive an Indifference Curve (IC) from a Utility Function (UF)?

Answer 2

1. Set the utility function equal to a constant, U(x1,x2)=kU(x1,x2)=k.
2. Solve the equation for one of the goods (e.g., solve for x2x2 in terms of x1x1).

Question 3

What is the two-step procedure to derive a Demand Function (DF)?

Answer 3

1. Get the optimal bundle by setting the MRS equal to the price ratio (BRS=p1/p2BRS=p1/p2).
2. Substitute this result into the budget constraint to solve for the demand of each good.

Question 4

What are the steps to calculate Compensating/Equivalent Variation?

Answer 4

1. Multiply prices by the given demand function values.
2. Plug these values into the utility function.
3. Find the new income mm by equating this new utility level with the original utility level from the initial optimal bundle.
4. Subtract this new mm from the original income.

Question 6

What is the standard form of the Budget Constraint?

Answer 6

m=p1x1+p2x2m=p1​x1​+p2​x2​

Question 7

What is the equation for the Substitution Effect?

Answer 7

x1(p′,y′)−x1(p,y)x1​(p′,y′)−x1​(p,y)
(Change in demand when utility is held constant at the new prices)

Question 8

What is the equation for the Income Effect?

Answer 8

x1(p′,y)−x1(p′,y′)x1​(p′,y)−x1​(p′,y′)
(Change in demand due to the change in purchasing power, holding the new prices constant)

Question 9

What is the Slutsky Identity in terms of total change?

Answer 9

δx=δxs+δxnδx=δxs​+δxn​
(Total Effect = Substitution Effect + Income Effect)

Question 10

What is the Slutsky Equation in terms of derivatives?

Answer 10

∂x∂p=∂xs∂p+∂xm∂m⋅x1∂p∂x​=∂p∂xs​+∂m∂xm​⋅x1​

Question 12

What is the general formula for Price Elasticity of Demand?

Answer 12

e=∂q/q∂p/pe=∂p/p∂q/q​ or e=pq⋅∂q∂pe=qp​⋅∂p∂q​

Question 13

What is the formula for Arc Elasticity?

Answer 13

Uses average price and quantity:
%ΔP=2hPnew+Pold%ΔP=Pnew​+Pold​2h​
%ΔQ=Qnew−Qold(Qnew+Qold)/2%ΔQ=(Qnew​+Qold​)/2Qnew​−Qold​​
Elasticity = %ΔQ%ΔP%ΔP%ΔQ​

Question 14

What is the formula for Point Elasticity at a point (x1∗,p1∗)(x1∗​,p1∗​)?

Answer 14

e=(p1x1)⋅(dX1dp1)e=(x1​p1​​)⋅(dp1​dX1​​)

Question 15

What is the formula for Income Elasticity of Demand?

Answer 15

∂x1/x1∂m/m∂m/m∂x1​/x1​​

Question 16

What is the Adding-Up Condition for income elasticities?

Answer 16

s1⋅em1+s2⋅em2=1s1​⋅em1​+s2​⋅em2​=1, where sisi​ is the budget share of good ii.

Question 18

What is the budget constraint in the labor supply model?

Answer 18

pC+wR=wR‾+mpC+wR=wR+m
where CC is consumption, RR is leisure, R‾R is total time, ww is wage, and mm is non-labor income.

Question 19

What is the Revenue Function for a firm?

Answer 19

R(p)=p×x∗(p)R(p)=p×x∗(p)
(Price times the profit-maximizing quantity supplied)

Question 20

What is Marginal Revenue when expressed as a function of price, MR(x(p))MR(x(p))?

Answer 20

dRdp=x(p)[1+e]dpdR​=x(p)[1+e]
where ee is the price elasticity of demand.

Question 21

What is Marginal Revenue when expressed as a function of quantity, MR(p(x))MR(p(x))?

Answer 21

dRdx=p(x)[1+1e]dxdR​=p(x)[1+e1​]

Question 23

What is one method for computing the decrease in consumer surplus (non-monetary)?

Answer 23

CS=R+TCS=R+T
Or, for a linear approximation, use the area of a trapezoid: (a+b)2⋅h2(a+b)​⋅h