Households utility function is U(c, l) = ln(c) + 4 ln(l) and budget constraintis c = (1 − t)hω + π, in

which h = 1 − l and t = 0.2 is a a flat rate tax rate

that is used to finance a wasteful government expenditure G. Output is produced by

a firm with technology Y = 1000H.

(a) (5 points) Find firm’s labor demand function, i.e., draw it in a graph. (You

could read more about it on page 176 and 177 of the book).

(b) (5 points) What is the equilibrium wage in this economy?

(h) by household and household utility (u(c, l)).

(d) (5 points) Find quantity of labor demanded by firms (H), output (Y ) and government

expenditure (G) in the equilibrium.

3. (25 points) Consider the economy in the previous question. A new government

is in office and thinks it is “unfair” for labor income of the household to be taxed

away. The government decides to finance its expenditures by taxing the “greedy

corporations”. Government increases tax rate from 0.2 to 0.25 and ask employers to

pay it. Therefore, for each unit of labor that firms hire at wage ω, they have to pay

ωt to the government (t = 0.25).

(a) (5 points) Write the firm’s profit problem and the household’s budget constraint.

(b) (5 points) What is the wage rate in this economy? What is the firms profit at

that wage?

(h) by household and household utility (u(c, l)).

(d) (5 points) Find quantity of labor demanded by firms (H), output (Y ) and government

expenditure (G) in the equilibrium.

(e) (5 points) What is the effect of new tax policy on household?s welfare and

government expenditure? Is the policy effective in making households happier?