$1.$ Investment Decision $(8$ points$)$

Suppose a business owner is trying to decide whether to invest in a new piece of machinery. The machine costs $$500,000,$ and it is expected to generate revenue of $$650,000.$

Complete all two parts $($a$-$b$).$

a$.$ Solve for the expected rate of return on this machine.

b$.$ If the interest rate the business owner has to pay is $28\%,$ will the business owner buy this machine?

$2.$ Multiplier Effect $(15$ points$)$

Complete part a$.$

a$.$ During a recessionary gap, is the goal to increase or decrease the equilibrium GDP$?$ Will the change in spending be greater than, less than, or equal to the change in the equilibrium GDP$?$

Complete parts b$,$c$,$d

b$.$ In a given economy with an MPC of $0\mathrm{.}8,$ the equilibrium GDP equals $$225,000.$ If Xn decreases by $$25000,$ solve for the new equilibrium GDP that will result.

c$.$ In a given economy, with an equilibrium GDP of $$420,000$ both government purchases and taxes increase by $$30,000.$ Solve for the new equilibrium GDP that will result from these two changes.

d$.$ What is the relationship between the multiplier and the MPC$?$