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Introduction to Economics
(Code 102341) Universitat Aut`onoma de Barcelona Bannikova Marina, Fall 2017
Midterm Exam. Example.
25th of October 2017
Permutation 2.
PART 1. Test questions. Each correct answer adds 1 point, no-answer adds 0 point, an incorrect answer extracts 0.25 points. This part represents 60% of the final grade of the midterm exam.
- Assume two countries: country A and country B. They both produce apples (good x) and peaches (good y). Both countries have 12 working hours available. Country A can produce 1 apple using one working hour, and to produce 1 kg of peaches they need 3 working hours. On the other hand, we know that the production possibilities frontier of country B with the respect to apples and peaches is given by the equation y=6-x/2. Which of the following statements is true: a) Country A has an absolute advantage in production of peaches. b) Country A has both comparative and absolute advantage in production of peaches. c) Country B has both comparative and absolute advantage in production of peaches. d) None of the above is correct.
Comment. For the country A we can calculate the maximum production. In 1 hour they produce 1 apple, then in 12 given hours they can maximum produce 12 apples. Given that in 3 hours they produce 1 kg of peaches, it means that in 12 given hours they produce maximum 4 kg of peaches. The country B maximum production of apples is 12 (so that they do not produce peaches, that is y = 0, then by PPF 0 = 6 − x/ 2 ↔ x = 12); and their maxi- mum production of peaches is 6 (so that they do not produce apples, that is x = 0, y = 6 − 0 /2 = 6). Therefore, no country has an absolute advantage in production of apples, country A has a comparative advantage in apples and country B has an absolute and comparative advantages in production of peaches.
- Suppose the government of one federal state, which includes two states A and B, wants to make a reform of financial system of the two states. In particular, they have 1000 millions of euros to divide among the two states. Given this situation, which of the following statements is true: a) Giving 1000 million to state A is an inefficient assignment. b) Giving 3 / 4 of 1000 million to state A and 1 / 4 of 1000 million to state B is an efficient assignment. c) The only efficient assignment is to divide 1000 million equally between the two states. d) Giving 400 million to state A and 400 million to state B is a feasible and efficient assignment.
Comment. Any assignment that distributes the whole amount of the money between the two states is efficient. So, answer (a) would be correct if it would name it efficient; answer (c) is wrong telling that it is the only efficient assignment; answer (d) is not efficient since it does not distribute the whole amount of money.
- Imagine that simultaneously has happened the two following events that affect the market of Lambrusco (assume that it is an inferior good): (1) the income of the consumers has increased significantly, and (2) there was a small disease that has reduced a little bit the quantity of grapes (which is needed to produce Lambrusco) and therefore its price has increased slightly. The first event has a greater impact that the second one. What will happen with Lambrusco market? Suppose that both the demand and the supply fulfil the law of demand and the law of supply. a) Lambrusco will be more expensive and the quantity sold will decrease. b) Lambrusco will be cheaper and will be sold less bottles. c) It will be sold less bottles if Lambrusco but we cant determine if the price will rise or fall. d) Lambrusco will be cheaper and it will be sold more bottles.
Comment. The increase in income will shift the demand curve downward (to the left) reflecting the fact that when the income increases then the quantity demanded of an inferior good is decreasing. The grape disease will shift the supply curve to the left reflecting the fact that now the primary resource for producing the good got more expensive. The situation tells that the shift of the demand curve is greater than the shift of the supply curve, which is represented in the following graph.
Consider a general formula of elasticity: Ed =
dQD dP
P 0
Q 0
. The law of demand tells us that if the price increases, the quantity demanded decreases. Price goes in the numerator and quantity goes in denominator, therefore, with the increase of the price the elasticity increases.
- Choose an INCORRECT statement:
a) The rent elasticity of the demand indicates how will change the quantity demanded of a certain good with the variation of the income of the consumers. b) The cross price elasticity of the demand indicates how will change the quantity demanded of a certain good with the variation of the price of the other good. c) The price elasticity of the demand takes different values depending on the price that we take into account when do the calculation. d) When the demand is given by a linear demand function (so that it is a straight line), the price elasticity of the demand is always constant.
Comment. The price elasticity can be constant only for non linear demand functions.
- Suppose a market in an equilibrium, where the functions of the demand and supply fulfil the laws of the demand and supply, respectively. The government decides to fix a minimum price of the good greater than the equilibrium price. In this case it is true that: a) There will be an excess in demand. b) The producer surplus will not be affected. c) The consumer surplus will decrease. d) The loss of the efficiency will be zero.
Comment. In the next graph it is represented the consumer surplus and its change (blue and purple area decreased to only purple area) with the minimum price fixed. The producer surplus in fact will decrease, too. There will be an excess in supply not in the demand. And definetly there will be loss of the efficiency
P
Q
D S
Pmin
- Suppose that a certain good is a normal good. The function of the demand fulfils the law of the demand but the supply of this good is perfectly inelastic. In this case, if there is an increase in income of the consumers, then it is true that in the new equilibrium: a) Both the equilibrium quantity and price will increase b) The producer surplus will increase. c) The equilibrium price will increase but it is not clear about the equilibrium. d) The producer surplus will decrease.
Comment. The next graph represents what happens in this case. The producer surplus will increase from purple area up to purple and blue are together. P
Q
D 1 D 2
S
P 1
P 2
- Suppose that a function of production is F (L) = L2, where L represents the working hours. In this case it is true that: a) The function F (L) has increasing returns to scale and the marginal output of labour is decreasing. b) The function F (L) has increasing returns to scale and the marginal output of labour is increasing.
PROBLEM. This part has a weighting of 40% on the final mark of the exam. The score of each of the sections is: a-1 point, b-2 points and c-1 point.
The demand function and the supply function of a given good are given by the equations qd = 27 − p and qs = 2p.
a) It is requested:
- Define the concept of market equilibrium.
- Calculate numerically the market equilibrium (price and quantity)
- Calculate numerically the producers surplus, the consumers surplus and the total sur- plus.
- Represent graphically the answers in the previous sections.
b) Suppose that the government introduces a tax of 3 dollars per unit of product exchanged (regardless of whether it is introduced on producers or on consumers).
- Calculate the new equilibrium (price paid by the consumer, price paid by the producer and the new quantity sold).
- Calculate government’s revenue and the part paid by producers and the part paid by consumers.
- Represent graphically the answer of the previous sections.
- Will there be a deadweight loss? Calculate your answer numerically and plot it graph- ically.
c) Suppose now that the government, instead of putting a tax on the initial equilibrium in section (a), decides to give a subsidy per unit of product sold of $3.
- Calculate the new equilibrium (price paid by the consumer, price paid by the producer and the new quantity sold).
- Calculate the cost for the government of the subsidy.
- Graphically represents the new situation after the subsidy indicating the price paid by the consumer, the price received by the producer and the cost of the subsidy for the government.
- Is there a deadweight loss? In case your answer is positive, calculate its value numeri- cally.
Solution.
a.1. Market equilibrium refers to the situation when the demand is equal to the supply for a certain good. That is, the quantity supplied coincides with the quantity demanded. QS = QD.
a.2. Equilibrium price: QS = QD ↔ 27 − p = 2p ↔ 3 p = 27 ↔ pe = 9.
Equilibrium quantity: Qe = 27 − 9 = 2 ∗ 9 = 18.
a.3. Producer surplus (gray triangle in the following graph): P S = 12 18 ∗ 9 = 81.
Consumer surplus (blue triangle in the following graph): CS = 12 (27 − 9)18 = 162.
a.4.
P
Q
27 D S
Qe = 18^27
Pe = 9 equilibrium
b.1. The new supply function is QS = 2(p − 3). Therefore, the new market equilibrium is pe = 11 and Qe = 16. Consumers pay 11, producers receive 11 − 3 = 8.
b.2. There are 16 units sold in the new market equilibrium, for each of these the government receives 3 dollars of tax. Therefore, T axRevenue = 16 ∗ 3 = 48.
Tax incidence on consumers (11 − 9) ∗ 16 = 32; tax incidence on producers (9 − 8) ∗ 16 = 16
b.3.
Yellow area: consumer surplus;
Orange area: producer surplus;
Blue area: tax incidence on consumers;
Red area: tax incidence on producers;
Gray area: deadweight loss of efficiency.
P
Q
27 D S SS
consumers pay 7
producers receive 10
c.4. Yes, there is, it is 12 (20 − 18) ∗ 3 = 3. it is the red triangle:
P
Q
27 D S SS
consumers pay 7
producers receive 10
