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.