Compared with Real Business Cycle, the New Keynesian Model adds Nominal Rigidity to the RBC model (other remain the same). This directly leads to the situation that output and employment are not at the optimal level. This model allows for Involuntary Unemployment.
Model
The model is very similar to Real Business Cycle, and also other similar models in Macroeconomics. It includes household, firms, and central bank.
Some assumptions:
Household
- consume baskets of goods and supply labour to firms
- save risk-free government bond (not capital here)
- owns firms and receive dividends (if they make profits)
Problem
subject to
- : since in the market there’s continuum of varieties indexed by . here is the quantity. Overall it means the total expenditure you spend on the goods in the market.
Why we don’t construct it as discrete? It’s because in this setting, each firm is a monopolistic competitor. Each firm produces a unique variety and has some pricing power, but it depends on the elasticity of substitution .
And people got utility from consuming this basket of goods, we have to introduce Constant Elasticity of Substitution (CES).
The optimality for household:
Optimal consumption and bond holdings (Euler):
Static labor vs consumption optimization:
- \frac {U _ {L , t} ^ {\prime}}{U _ {C , t} ^ {\prime}} = \frac {W _ {t}}{P _ {t}} $$ Optimal expenditure allocation $$ C _ {i, t} = \left(\frac {P _ {i , t}}{P _ {t}}\right) ^ {- \epsilon} C _ {t} $$ > See derivation from the MN4. ### Firms - Produce differentiated goods - Choose the price at which they sell their variety. > A specific firm only produces identical good, but still faces [[Monopolistic Competition]] ### Central Bank Set the nominal interest rate on government bonds ##