The economy is populated by 100 agents. Each agent has to divide 1 unit of time between work and leisure given the wage rate w paid on the labor market. In addition
to the salary, he or she also receives dividend a income of π = Π/100 (the total profit
of the firms Π is distributed equally among all the consumers in form of dividends)

Suppose that the government does not incur expenditures, so G=0.

The agent’s utility function depends on consumption (c) and leisure (l), and it is assumed
to satisfy u(c, l) = 0.5 ln(c) + 0.5 ln(l). On the other side of the market, there are
firms who hire workers and produce output. The representative firm operates with
a Cobb-Douglas production technology Y = zK^0.5N^0.5
, where z denotes the total
factor productivity, and K = 100 is a fixed amount of capital. Each of the firm’s
employees receives wage w, i. e. the total labor cost of the firm is equal to wN^d

Suppose that initially z = 1 (so the competitive equilibrium is the one we calculated
in class), but the economy is hit by a pandemic, which we can model as a decrease
in TFP: so z goes down to z = 0.5.

(a) What are the effects of this negative TFP shock on the equilibrium allocations
and prices? To obtain full credit, compute the value of all the endogenous
variables determined in equilibrium

(b) Does our model predict that the pandemic would cause a recession? What are
the effects of the pandemic in the level of employment? (ignore the fact that
some workers may get sick for the moment).

Now, suppose that the pandemic only affects the productivity of labor. This
can be modeled by letting z = 1 as in part a, but assuming that labor is less
productive,
Y = zK^0.5[ωN]^0.5
Assuming that the value of ω = 0.5, re-compute (a) and compare the new results
with your previous answer, providing some intuition.