Question

Suppose an economy is characterized by the following equations:

?=?+?? 789

? = ?7 + ?8? − ?;? ? = ?̅
? = ?<

?7 >0,0<?8 <1,?7 >0,0<?8 <1,?; >0,?8+?8 <1.?̅and?<areexogenousvariables(and positive). While doing this exercise, approach all parameters and exogenous variables as if they were known numbers.
a. Calculate the IS relation [Hint: You want to find a relation between ? and ? that establishes

equilibrium in the goods market. Here you can present it as an equation that has only ?on the left hand side and ? on the right hand side.]

b. Graph the IS curve in a graph with ? on the vertical axis and ? on the horizontal axis [Hint: In part (a), the IS relation is expressed with ?on the left hand side and ? on the right hand side. For this part, you may want to rewrite the IS relation to have ?on the left hand side and ? on the right hand side.]

c. Suppose the central bank chooses an interest rate: ? = ?̅ . Add the LM curve to your previous graph.

d. Solve for equilibrium output at that interest rate.

Answer 1