4 - Equilibrium with flexible Prices Flashcards
What is monetary neutrality?
Neutrality of money is the idea that a change in the stock of money affects only nominal variables in the economy such as prices, wages, and exchange rates, with no effect on real variables, like employment, real GDP, and real consumption -> monetary settings do not play any role for equilbrium determination of real economic variables
What is classical dichotomy?
classical dichotomy is the idea, attributed to classical and pre-Keynesian economics, that real and nominal variables can be analyzed separately
What is ε?
the elasiticity of substitution between different goods
What is MRSⱼ,ₖ in words?
The marginal rate of substitution between goods j and k = the rate at which a consumer can give up some amount of one good in exchange for another good
What is MRSⱼ,ₖ as formula?
MRSⱼ,ₖ = U𝒸,ⱼ / U𝒸,ₖ
What is U𝒸,ⱼ ?
the marginal utility with respect to good j
What is the definition of the elasticity of substitution between different goods?
\_ _d ln(Cₜ(j) / Cₜ(k) )_ d ln (MRSⱼ,ₖ)
What happens if ε goes to infinity?
The higher ε is the easier is to substitute between goods. In the limit, when ε → ∞, we have an
infinitely elastic demand.
i.e., an infinitely elastic demand leads to a situation without markup, and as with perfect competition, the prices equal the marginal costs of production.
What are the assumptions in an equilibrium with flexible prices?
- imperfect competition: assume that each firm produces a differentiated good.
- In an equilibrium with flexible prices and wages, real variables are uniquely determined and independent of monetary policy
What is this?
definition of consumption (=”quantity of the consumption basket”) of households under flexible prices
What is this and what are its properties?
definition of price index under flexible prices (prices of all goods)
properties:
- If the prices of two goods are the same, their price index is the same
- If you multiply prices by a constant price index is also multiplied by a constant
What is this?
The budget constraint of the households’ optimization problem under flexible prices
What is the definition of consumption (=”quantity of the consumption basket”) of households under flexible prices?
What is the definition of price index under flexible prices?
What is the budget constraint of the households’ optimization problem under flexible prices?
What is so special about this result, what does it mean?
It is the budget constraint of the households under flexible prices - and if the result holds, the maximization problem for many households under flexible prices is the same as with one household
What does (i) denote in this specific production function?
the specific good that firm i produces at period t
What is the cost of prodcing Yₜ for firm i if wage Wₜ is given under flexible prices?
What are the nominal marginal costs for firm i under flexible prices and how do you get there?
differentiating the cost of producing Yₜ with respect to Yₜ
How do you get to the real marginal costs from the equation below, in a setting of flexible prices?
dividing by Pₜ:
How is the (log) markup of firm i under flexible prices defined?
How can definition of the average (log) markup of firm i under flexible prices be rewritten (holding up to a first order Taylor approximation)?
Using the first order Taylor approximation of the price index, it can be simplified as follows
How is the goods market clearing (=equilibrium) defined under flexible prices?
What do these equations represent?
Setting: monopolistic competition in the classical economy with flexible prices and wages
Equations: Maximization problem + constraints of firm
How can you interpret this lagrange multiplier of the firm’s maximization problem in monopolistic competition?
- It is the lagrange multiplier attached to technology and represents the marginal costs.
- -> the marginal relaxation of the technology constraint means “one extra unit of output without needing to produce it”
- -> but because of the binding demand constraint, the interpretation would rather be that the firm produces one unit less to take advantage of this -> the saving value associated with this is the marginal costs
If this is the optimal price in the equilibrium with flexible prices, what does e/(e-1) represent?
markup that the firm can extract
How can the the logarithmic optimal price be written as (under flexible prices and wages)?
Where does the the (logarithmic) real marginal cost below stem from?
It comes form the logarithmic optimal price under flexible prices and wages:
What does each of these equations represent?
1) logarithmic real marginal costs = negative markup
2) equilibrium output in flexible prices+wages
3) equilibrium hours
4) equilibrium real interest rate
* Note: Money is neutral in this model. (Even in the short-run!)*
What is this equation called?
goods market equilibrium
What is this equation called?
production function
What is this equation called?
expression for real marginal costs
How is this equation derived?
What is this equation called?
new IS-curve
How is this equation derived?
see below + log linearization
What is this equation called?
real money demand
Show that employment is a function of technology, aₜ, if the real marginal cost is equal to a constant markup, -μ.
Show that output is a function of technology, aₜ, if the real marginal cost is equal to a constant markup, -μ.
Show that the real interest rate is a function of technology, aₜ, if the real marginal cost is equal to a constant markup, -μ.
