PART 1Exercise 1: Supply and Demanddemanded quantitysupplied quantityprice

2400

2041

1682

12123

8164

4205

0246

1. Draw the appropriate supply-demand diagram. P

566Supplyy

4DemandE

3

12

Q2412

2. Calculate the equilibrium price and quantity?P* = 3 & Q* = 123. Assuming that the price is 2, does an over-supply or under-supply thus prevail?

Under supply

4. Assuming that wheat becomes scarce due to a storm. The following should apply: Demanded quantitysupplied quantityprice

2400

2000

1600

1241

882

4123

0164

Map the new supply function in the diagram. What is the equilibrium price now? P* = 2 & Q* = 8P

4Supplyy

3DemandE

2

1

Q168

5. Explain, with the help of a diagram, why the equilibrium price for hotel prices on the Adriatic would decrease if the weather from now on was very warm in Northern Germany every summer. => Because Nothern Germany is so cold, thus when it is very warm now, the demand of tourists to visit the place will increase; as a result the number of travellers to Adriatic will fall and this leads to reducing prices of hotel too.

Exercise 2: Budget amounts

Show, by means of a sketch, how the budget amount changes with 1. A price increase of commodity 1.

C = (I/Pc) (Pf/Pc) * F The budget line rotates inward to line 2 because the persons purchasing power has diminishedC2

L1

L2

C1

2. A decrease in budget.

C2

L1

L2

C1

If the income decreases, the budget line shifts inward from L1 to L2

3. An introduction of quantity tax on commodity 1.

L1

L2

C1

Price on C1 increases a decrease in purchasing power

4. An introduction of value tax on all commodities. C2

L1

L2

C1

Prices of two goods go up slopes or the ratio of 2 prices unchanged shifting the budget line inward

5. InflationC2

L1

L2

C1

Prices of two goods increase at the same ratio with inflation, income is constant => purchasing power decreases ( slope unchanged, intercept shifted downward)

C2

C1

If both prices and income changed or rise proportionately will not affect to the budget line or purchasing power

6. A rationing of commodity 1. C2

AD

L1

C1

E

BQ

A

7. A minimum quantity of commodity 1 necessary for survival (should the consumer consume less than this minimum amount, then they must die). A

DA

L1

EB

C1

Q

8. An introduction of value tax on the consumption of commodity 1 outside of a minimum quantity.

DAA

I - Q

L1

L2B

EC1

Part II:Exercise 1: Preferences1. Explain the relationship between preferences and utility functions. 2. Explain the difference between cardinal and ordinal utilities. 3. Explain why any positive monotonous transformations of a utility function depict the same preferences (deleted)

Exercise 2: Required optimality condition Show graphically and mathematically (by using the Lagrange approach) that the slope in the budget line is equal to that of the slope of the indifference curve at an optimum, that thus

applies. Interpret the condition.OptimalC1Q1C2

1. The method of Larange Multipliers = U(x1, x2) (P1x1 + P1x2 I)Where: P1x1 + P2x2 I = 02. Differentiating the Lagrangian = MUx1(x1, x2) P1 = 0 = MUx2 (x1, x2) P2 = 0 = I P1x1- P2x2 = 03. Solving the resulting equations MUx1(x1, x2) = P1MUx1(x1, x2) = P1I = P1x1+ P2x2 The equal marginal principle = =

= =

Exercise 3: Indifference curves and demand Mr. K consumes two commodities: honey (commodity 1) and coffee (commodity 2). His utility function is as follows:

Utilize prices and for the drawings and income. 1. What functional forms do the indifference lines have? Produce a sketch.

With U (x1, x2) = x1(1+x2) + x2Or U (x1, x2) = x1 + x2(x1 +1) x1 = x2 = Taking 1st and 2nd derivatives < 0

2 (U + 1)(x1+1) -3 > 0

2. Name various utility functions with the help of which we can deduce these preferences.

U(x1, x2) = A.U(x1, x2) = A()U(x1, x2) =

3. Calculate the marginal rate of the substitution for any bundle of goods (,). MRSX10, X20 = = = =

4. Assume that Mr K. has and . He receives an offer to deliver a (marginal) unit of and in exchange receive two (marginal) units of . Does he agree? Form an argument using the marginal rate of the substitution. What would be the case if he received the offer at position (2,3)? MRS = = 3 > 2 DISAGREEMRS = AGREE5. Define & calculate the demand functions. Are the demand functions homogeneous in(a) income? (b) in income and prices? U(x1, x2) = x1 + x1x2 + x2E = P1x1 + P2x2 P1x1 + P2x2 E = 0 = U(x1, x2) (P1x1 + P2x2 E) (1) = 1 + x2 P1 = 0 = 1 + x1 P2 = 0 = E - P1x1 - P2x2 = 0 (2) = = X2 = (1+X1) 1 (3)

Substituting (3) into (2) E P1x1 (P2 * ( (1+x1) 1)) = 0 X1 = (4)E 2P1x1 P1 + P2 = 0So, x2 = (5)

(b) income and prices?f(x) = tf(x)x1(P1, P2, E) =

x2(P1, P2, E) =

x1(P1, P2, E) = =

The same to x2=> Changes in income, the demand functions are not homogeneous=> In contrast, when both income and price change, it gives rise to be homogeneous in the functions

6. Define, calculate and draw the Engel curves. Definition: Engel curve relating the quantity of a good consumed to income

E1= 2P1x1 + P1 P2 = 4x1 + 1E

9

5X1

21

E2 = 2P2x2 + P2 P1 = 2x2 -1

3

1X2

21

7. Define, calculate and draw the income expansion path. (=income consumption curve) Income consumption curve: curve tracing the utility maximizing combinations of two goods as a consumers income changes(1) E1 = E2 4x1 + 1 = 2x2 1 X2 = = 2x1 + 1 (*)Maximizing utility (one of the properties of demand curve) (2) MRS = P1/P2 = = 2 1 + x2 = 2 + 2x1 => x2 = 2x1 + 1 (**)We have, (*) = (**) => optimalX21

1

X1

X2

X1

8. Define normal and inferior commodities. Are we talking about normal or inferior commodities here for both commodities?

Normal goods: consumers want to buy more of them as their incomes increase. When the income- consumption curve has a positive slope, the quantity demanded increases with income. As a result, the income elasticity of demand is positive > 0

Inferior: consumption falls when income rises. The income elasticity of demand is negative < 0

= > 0=> NORMAL COMMODITIES = > 0

PART III:Exercise 1: Income and substitution effect

The Slutsky equation for "Cobb-Douglas" preferences:

A consumer has the utility function . The consumer's income is E and the prices of both goods are and . Sketch the indifference curve and solve the following exercise graphically and mathematically. U = x1 x21- => x21- = x2 = =

= < 0

= > 0X2

X1

Max U (x1, x2) = x 1 x21- P1x1 + P2x2 E P1x1 + P2x2 E 0 E - P1x1 - P2x2 0

1. Calculate the demand for commodity 1 and 2.

= u(x1, x2) (P1x1 + P2x2 E)Or = u(x1, x2) (E - P1x1 - P2x2) = x 1 x21- (P1x1 + P2x2 E) = x -11 x21- - P1 = 0

= (1- ) x 1 x2 - P2 = 0

= E P1x1 - P2x2 = 0

x -11 x21- = P1 (1- ) x 1 x2- = P2

= =

X2 = (*)

Substituting (*) into E - P1x1 - P2x2 = 0

E P1x1 P2 = 0 = E => x1* (P1, P2, E) = Replace x*1 into X*2 => X*2 =

2. Assume the price of commodity 1 decreases from to.What now is the demand for both commodities?

X1(, p2, E) = > x1 (P1, P2, E)

X2(, p2, E) = = x2 (P1, P2, E)

3. How large would the corresponding income have to be for a consumer to just be able to afford the original bundles of goods? Also produce a sketch. E = P1X1 + P2X2 E = + => E =P1 P1 > 00 < E < EX2

C

AB

X1