3. Consider an economy with two agents (agents a and b), two goods - labor/leisure and a consumption good - and two firms. Both firms transform labor into the consumption good. Firm 1,

with production function y1 = f(L1), belongs to agent a, and firm 2, with production function

y2 = g(L2), belongs to agent b. (L denotes a quantity of labor and y a quantity of consumption

good produced). Each agent has 3 units of time which can be used as leisure or sold as labor.

Firm 2 uses a technique of production which creates a negative externality z, a chemical which has

an adverse effect on the consumers and whose quantity is proportional to the level of production:

z = y2. The utility and production functions are as follows

ui(`i

, xi

, z) = p

`ixi

1

8

z, i = a, b, f(L1) = L1, g(L2) = 2p

L2

where ` denotes leisure and x the quantity of consumption good.

(a) Derive the competitive equilibrium of this economy, i.e. equilibrium prices, production and

consumption plans. [Restrict attention to allocations where both firms produce a positive

amount.]

(b) To show that the equilibrium is not Pareto optimal consider the following marginal change

from the equilibrium allocation: add /2 of leisure to each agent and decrease the labor

used by firm 2 by . Decrease equally the consumption of the consumption good of the two

agents. Do not change anything to firm 1's plan. Compute the marginal change in utility for

each agent and show that both agents are better off. Explain. [It may be easier to keep the

partial derivative notation for estimating the change in utilities and then evaluate the values of these

derivatives at the equilibrium.]

(c) Assume that the government fixes a limit z

on the amount of pollution emitted by firm 2.

Solve for the 'regulated competitive equilibrium' as a function of z

. [Assume that z

is

smaller than the value found in (a)].

(d) To find the optimal z

come back to your calculations in (b) and find the value of z

such

that the change considered in that question (or the reverse when < 0) cannot improve the

utilities of the agents.

(a) State and explain four economic influences on an individual firm's demand for labour. (25)

(b) Explain, with the aid of a labour market diagram in each case, how equilibrium wage rates are

determined in:

A free labour market;

A labour market where a trade union has negotiated a minimum wage. (25)

(c) Women in Ireland earn on average 17.1% less per hour than men, according to a study by the

European Commission (Tackling the gender pay gap in the European Union, 2011).

(i) Outline two possible reasons for the lower wage rates earned by women in the Irish

economy.

(ii) Outline one measure that could be taken to close the gender pay gap. (15)

(d) Explain briefly Karl Marx's economic theory about the exploitation of labour in a capitalist

system.