– Answer clearly to all questions- Must contain full solutions.

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● must contain full solutions! Correct answer without the solution or with wrong solution, will earn

0 points.

1. Suppose that consumer is spending all his income on goods A and B. The price per unit of good

A is 8 euros and the price per unit of good B is 4 euros. Consumer’s income is 1000 euros.

a) Describe the consumption possibilities of this consumer by the budget line equation. (Use A to

denote the quantity of good A and use B to denote the quantity of good B) (NB! Only the budget

line equation is required. Graph is not required.)

b) Find the opportunity cost of consuming 10 units of good A for this consumer (measured in terms

of units of good B). (5 points)

2. Describe the preferences of the consumer for whom one cup of coffee is always substitutable

with two cups of tea

a) mathematically (by the utility function) (5 points)

b) graphically (by the indifference curves) (5 points)

(Please denote the quantity of cups of coffee by letter C and the quantity of cups of tea by letter T.

Don’t forget to label the horizontal and vertical axis and identify the numerical values of intercepts).

3. The consumer’s utility function is U(x,y) = xy2 , where x denotes the quantity of good X that the

consumer consumes and y denotes the quantity of good Y that the consumer consumes. The price

per unit of good X is 8 euros and the price per unit of good Y is 4 euros. Consumer’s income is 240

euros.

a) Find the marginal utility of good X and the marginal utility of good Y for this consumer. (5

points)

b) Find the optimal quantity of good X and good Y for this consumer. (10 points)

4. The consumer’s utility function is U(a,b) = a + 4b, where a denotes the quantity of good A that

the consumer consumes and b denotes the quantity of good B that the consumer consumes. The

price per unit of good A is 10 euros and the price per unit of good B is 8 euros. Consumer’s income

is 1600 euros. Find the optimal quantity of good A and good B consumed by this consumer. (10

points)

5. Consumer’s utility function is U(X,Y) = min {x; 5y}, where x denotes the quantity of good X

that the consumer consumes and y denotes the quantity of good Y that the consumer consumes. The

price per unit of good X is 4 euros and the price per unit of good Y is 10 euros. The consumer’s

income is 600 euros. Find the optimal quantity of good X and good Y consumed by this consumer.

(10 points)

6. The consumer’s demand for good X is determined by the function X (Px, M) = M / 2Px , where

Px denotes the price per unit of good X. Consumer’s income is 480 euros, the price per unit of good

X is 10 euros. If the price per unit of good X increases by 2 euros (thus, the new price per unit of

good X is 12 euros), then

a) Calculate the total change in the quantity of good X demanded by the consumer? (3 points)

b) Calculate the substitution effect (denote it by xs) and the income effect (denote it by xM)

associated with this price increase of X according to Slutsky approach. (7 points)

7. Suppose that a consumer is facing following offers: Offer 1: receive today 4400 euros and

receive 2200 euros exactly in one year Offer 2: receive today 1500 euros and receive 5500 euros

exactly in one year Which offer would the rational person accept if:

a) the nominal annual interest rate is 10% and the expected inflation is 0%. (5 points)

b) the nominal annual interest rate is 25% and the expected inflation is 0%. (5 points)

Let’s assume that the choice between these two offers does not affect the offers made for this

individual in the future. Suppose also that the interest rate applies both, for lending as well as for

borrowing.

8. Market demand for good Y is described by function YD = 250 – 6PD, where PD is the demand

price and YD is the quantity of good Y demanded. Market supply of good Y is given by function

YS = 4PS, where PS is the supply price and YS is the quantity of good Y supplied.

a) Find the market equilibrium quantity and equilibrium price. (5 points)

b) Suppose that a tax 5 euros is applied per unit of good Y, while the rest of the factors that could

affect demand or supply remain unchanged. Find the market equilibrium (the equilibrium quantity,

the demand price and the supply price) that will exist in this market after this tax. (5 points)

9. The consumer’s demand for good X is described by the function x = 400 – 5Px, where x denotes

the quantity of good X demanded and Px is the price (in euros) per unit of good X.

a) Calculate the consumer’s (net) surplus from consuming good X, when price of X is 30 euros.

Illustrate the consumer’s (net) surplus in the graph. Mark clearly the area that corresponds to the

consumer’s (net) surplus and identify (on the graph) all the numerical values that are important for

calculation of the consumer’s (net) surplus in this exercise. (7 points)

b) Suppose that the price of good X decreases from 30 euros to 20 euros. Calculate the change in

the consumer’s (net) surplus associated with this price decrease. Illustrate this change in consumer’s

(net) surplus in the graph. Mark clearly the area that corresponds to the change in the consumer’s

(net) surplus and identify (on the graph) all the numerical values that are important for calculation

of the change in the consumer’s (net) surplus in this exercise. (8 points)

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