Answer to Question #42658 in Macroeconomics for Amaar

Question

An economy’s marginal propensity to consume out of disposable income is 0.75, its
marginal and average tax rate is 0.15, and its marginal and average propensity to import
is 0.15. What is the increase in government expenditure needed to prevent a fall in
equilibrium income of 20 billion Dollar?

Answer 1

A. EC = 730Q −6.5Q2 and the cost of abatement of the same pollution is 
CA = 11Q2 +1020Q, where Q is the quantity of the air pollutant emitted. (Hint: MEC and MCA).
i. The optimal amount of emission fee per unit of pollutant that is in the point, where MEC = MCA.
MEC = EC' = 730 - 13Q
MCA = CA' = 22Q + 1020
730 - 13Q = 22Q + 1020
9Q = -290
Q = -32.2 units must be imposed to ensure an efficient level of air pollution.
ii. The values of total emission fee that the firm will pay and the total abatement costs that the firm will incur if it produces the optimum amount of air pollutant are:
EC = 730*32.2 - 6.5*32.2^2 =  $16,755.5
CA = 11*32.2^2 + 1020*32.2 = $44,249.2.