Esercizi di Topics in Economics and Project Valuation

d) Calculate the variation in consumer surplus that results from the introduction

of the tax. Assuming that the t o t a l cost savings relative t o me di ca l ca r e

thanks to the t a x introduction is 5,000 EUR, discuss whether this measure is

efficient.

[qi*LR LR

=5 (MC=AC); n =100; Q**=490, n'=98; var surp cons = - 4950; measure is efficient because the loss

is more than offset by savings in health care costs]

Exercize 7

Firm Alfa produces good X and is the sole producer in the market. Its total production

costs are: 2

C(X)= X

The market demand is: D

X = 400 - p

where p is the price.

Determine:

a) the equilibrium price and quantity;

b) the firm’s profit;

c) total surplus.

Assume the Government decides to provide a subsidy to consumers equal to 40 per

unit purchased.

d) Determine the new equilibrium price and quantity.

e) What is the price paid by consumers net of the subsidy?

f) Calculate the firm’s profit in this setting.

g) Determine total surplus in the situation described at point (d).

[X*=100, p*=300; Π=20000; total surp 25000; X**=100, p**=330, p =290; Π =24200; cons.

paid s

surp =6050, prod. surplus =24200, subsidy cost=4400, total surp =25850]

s s s

Exercize 8

Mattia’s income is I=8. Mattia spends his income in buying commodity x and

commodity y. His utility function is: U(x,y)= x + y.

The unit price of commodity x is p = 1 and the unit price of commodity y is p = 2.

x y

a) Determine Mattia’s equilibrium bundle.

b) Suppose the price of good x increases to p = 4. Determine the new

x

equilibrium bundle.

c) Given the new equilibrium bundle, determine the income effect and the

substitution effect.

d) Plot the demand curve for commodity x. Discuss your answer.

[E*(8,0); E**(0,4); x=0 for p >2, horizontal for p =2 up to x=4, decreasing curve for p <2]

x x x

Exercize 9

Firm A produces a specific type of paint X. The formula for producing 1 unit of paint

X involves mixing 2 units of A and 1 unit of P (inputs are used in fixed proportions).

a) Represent the isoquant map.

b) The price of A is p =5, the price of P is p =4. Determine the cost incurred by A

A P unit

to produce 100 units of paint X in equilibrium and the firm’s profit if the

price of x is p =17.

X a different input, P ,

c) Consumers require a more durable paint, for which is

n

The unit price of Pn is p = 8. Determine the cost incurred

needed. by A to

Pn

100 units of x in this case.

produce

d) Determine the minimum unit price the firm will have to charge not to shut

down

[non substitutable inputs; X=min0.5A,P P vertical axis, A horizontal axis (vertexes along

P=0.5A); if X=100 then A=200 and P=100, C=1600 and Π=100; p=18]

Exercize 10

Firm A is a price-taking firm, produces commodity y and exhibits the following

long-run total

cost function: 2

C (y) = 4y + 0.25

for y>0.

The market demand curve is:

D

y = 300 - 50p

where p is the price of commodity y.

a) Calculate long-run marginal costs and long-run average costs.

b) Calculate the long-run equilibrium price and quantity and the number

of firms operating in the market.

Assume now that the demand curve becomes:

D

y = 750 - 150p.

c) How do the equilibrium price and quantity vary?

d) How much will firm A produce in equilibrium? How many firms will be

operating in the market? yi

[MC =8y, AC =4y+1/(4y); y*=1/4, p*=2, Y*=200, n=800; p**=2, Y**=450; **=1/4, n**=1800]

LR LR

Exercize 11

100 homogeneous firms are operating in a competitive market. Their marginal

costs

are: i

MC = 5 + 0.5 y i

where y represents the quantity produced. The market demand curve is:

i Y = 11.000 - 40p

where Y indicates the total quantity purchased by consumers.

a) Determine the market supply curve, the short-run market equilibrium price

and quantity, and the i-th firm’s s optimal output level.

b) Assuming that the i-th firm’s production costs are:

2

C = 5y + 0.25y

i i

and that the fixed input has a non-null opportunity cost exclusively in the long

run (i.e., 4000), calculate the firm’s short-run profit.

c) Is the above equilibrium a long-run equilibrium? Discuss your answer.

[YS yi πi

=200p - 1000, p*=50, Y*=9000, *=90; =2025; it is not a long-run equilibrium, the firm’s

profit will be negative in the long run]

Exercize 12

Firm ALFA is a monopolist and produces commodity y. Its total cost function is:

da: 2

C = 8y + 2y

whereas its demand function is: P = 20 - 2y.

a) Determine the equilibrium price and quantuty the the firm’s profit.

The Government decides to introduce a tax T=2y on the output produced.

b) Determine the equilibrium price and quantity.

c) Provide your answer assumin thta the taxi is imposed on profits. Motivate your

answer. =9;

[y*=3/2, p*=17, y**=5/4, p**=17.5; price and quantity would not change]

Exercize 13

In a competitive market the market supply curve is:

Q= -10+2P,

the market demand curve is: Q = 50 - 1/(2P).

a) Determine the equilibrium price and quantity.

b) The Government introduces a tax on producers equal to 5 euros per unit of

output produced. Determine the new equilibrium quantity.

c) Represent in a graph the net loss generated and illustrate how to calculate it.

[Q*=38, P*=24; Q**=36; net loss=5]

Exercize 14

The production function of commodity Q is the following:

Q=2K+5L.