## EC201 MT definitions

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# Find uncompensated demand with Quasilinear utility. I.e. utility function of form u(x1,x2)= V(x1) + x2

1. State problem.
Utility function.
Budget contraint.
Non-negativity constraint.

2. What is the solution a function of?
Prices and income

3. Check for nonsatiation and convexity.
Nonsatiation - partial derivatives strictly greater than zero
Convexity - second derivative weakly greater than zero

4. USe tangency and budget line to find MRS=p1/p2
NB: as V is only a function of x1, MRS only depends on x1

5. Draw a diagram based on tangency and budget line conditions

6. Remember what you are trying to find

7. Write down equations to be solved
Budget line p1x1+ p2x2=m
MRS= p1/p2

8. Solve!

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Related Quiz Content
• What is a substitute?
If demand for good 1 increases when the price of good 2 increases then goods 1 and 2 are substitutes.

Cross price elasticity (p2/x1)(dx1/dp2) is positive
• What is a complement?
If demand for good 1 decreases when the price of good 2 increases then goods 1 and 2 are complements.

Cross price elasticity (p2/x1)(dx1/dp2) is negative.

Perfect complements have right angled indifference curves.
• Define compensated demand.
Compensated demand minimises the cost of obtaining the utilityu at prices p1 and p2 and is a function of utility u, p1, p2.
Notation:
h1(p1,p2,u) and h2(p1,p2,u)
• Find compensated demand.
1. Write down conditions.
Minimise expenditure p1x1+p2x2 subject to:
non-negativity contraints
utility constraint u(x1,x2)=...

2. What is the solution a function of?

3. Check for nonsatiation and convexity.

4. Use tangency and utility conditions MRS=p1/p2

5. Draw a diagram based on tangency and utility conditions.

6. Remind yourself what you are finding - compensated demand!

7. Write down equations to be solved
utility constraint
MRS=p1/p2

8. Solve!
• What is the expenditure function?
E(p1,p2,u) is the minimum amount you need to spend to get utility u at prices p1 and p2.

E(p1,p2,u) = p1.h1(p1,p2,u) + p2h2(p1,p2,u)
• What are 5 properties of the expenditure function?
1. Increasing in utility

2. Non decreasing in prices

3. Homogeneous of degree 1 in prices

4. Shephard's lemma

5. Concave in prices
• What is Shephard's lemma?
The derivative of the expenditure function wrt p1 equals the compensated demand for good 1
• What is the slutsky equation?
The total effect of change in price 1 on demand at constant income = substitution effect of change in price 1 on demand at constant utility - income effect of changein income on demand

the partial derivative of uncompensated demand of good 1 by p1 = the partial derivative of compensated demand of good 1 by p1 - (partial derivative of uncompensated demand by income) multiplied by uncompensated demand for good 1.
• What is the purpose of the Slutsky equation?
Working out how big income and substitution effects are.
• What is the base weighted price index?
quantities fixed at base

then p'x/ px

where p' is new price
• What is Laspeyres Price Index?
Same as Base weighted price index. Cost of getting bundle at new prices/ cost of getting bundle at old prices
EC201 MT definitions
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Definitions for the LSE course EC201 (Microeconomic Principles 1)
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