It is assumed that there is a firm that buys distinct goods produced by the intermediate goods producer, produces the marginal product and sells to marginal buyers by combining them1. The producer of the marginal product combines intermediate goods that are distinct and substitutable to each other based on the Dixit-Stiglitz aggregator defined in Eq. (4).

1 ⁄( ) (λ−1)

[∫ Yi λdj] = Y , (4)

where Yt is a marginal product, the intermediary goods Yti, are distinct and incomplete substitutions, and there is a static substitution elongation λt > 1 between them.

The profit maximization of the marginal products after the demand for the various types of intermediate goods is in the form of Eq. (5).

i −λt

Yti = [Pt] Yt, (5)

Pt

1 1−λt (1−λt)

where Pt = [∫0 (Pti) di] price index of marginal products of zero profit condition is obtained in the marginal goods sector and Pti is the price of all intermediate goods.

It is assumed that the economy consists of a large number of households that we show with i and that all of them are homogeneous. Households benefit from the use of goods, maintaining real balances of money, and by providing more work, their desirability decreases because their leisure will be reduced. The present value of desirability represented by a household during its lifetime is in the form of Eq. (6).

Households have the desirability of using marginal goods, Ct j, a and they have inadequacy due to the supply of work hours Nt j. They are the owners of capital, capital creation, and decision-makers of capital utilization. The form of the household utility function, which is a function of total household consumption, real money balance, and workforce supply, is given by Eq. (6).

c,t 1−σm 1−σ 1+η M

(Cj−bC ) (Nj) ( tc )

max 0 ∑∞ t=0 βt [ t t−1 − t + Pt ] . (6)

1−σ 1+η 1−σm

In which β∈ (0, 1) is the factor of discount, E0 represents the rational expectation factors using full information up to time t = 0, Ct j is the amount of marginal goods consumption. The parameters σ and η are positive; σ is the substitution pull reverse between consumption time. Parameter η> 0 is workforce supply relative to the actual wage in the utility function, and bε (0, 1) indicates the importance of consumption habits, which is the total consumption of the previous period. These habits depend on average economy per capita consumption. Therefore, every household is representative of the economy at time t when its consumption is larger; it receives more positive utility from more consumption, where b indicates how much the consumer

1 There are two methods for introducing monopoly competition using producers sell their distinctive goods to a competitive manufacturer the Dixit-Stiglitz index. First, we assume that producers of distinctive of the marginal product, whose production function is a CES goods directly sell their products to consumers, and consumers summation of these distinct goods. In this study, we chose the second combine these commodities based on the Dixit-Stiglitz index. method, but the choice of either of the two methods of analysis does Another way is to assume that chains of intermediate goods not affect the outcome of the analyses.

tends to smooth its level of consumption compared with the average per capita consumption of the past period. A higher b represents a higher degree of dependence on consumption habits.

Households maximize their utility according to the budget:

i c,i j j

i i i c,i d bt−1 mt−1 WtNt k j i i

ct + It + bt + mt = (1 + rt−1) πc + πc + P + [Rt ut − Ψ(ut)]Kt−1 + TRt − Tt + t t t (7) Divt i,

where sample household expenses for purchases of marginal consumer goods are (Ct j), It ii is the amount of investment, bi t is government bonds, rt d−1 epresents the nominal interest rate of government bonds, Tti is household taxes (direct, indirect, and value-added taxes), TRit government subsidies and households hold their wealth as mc t,iof the real balance of money and government bonds. Total income of households from wages

Wt i

( Pc Nt), is obtained by the lease of capital minus the cost of changes in the rate of utilization of capital capacity and dividends distributed by enterprises producing intermediate goods and banks Divt i. In Eq. (7), Wti is the nominal wage, Rk t is the actual return rate of capital and ut is the intensity of use (Operating rate) of capital capacity and Ψ(ut) is the cost of capital utilization.

The cost of using capital capacity Ψ(ut) represents the cost per unit of physical capital. In long-term equilibrium, relations are established. Ψ′′ > 0 , Ψ′ > 0, Ψ(1) = 0 , u = 1.

Capital stock is the ownership of households and is used as a homogeneous factor in the production process. Households lease their capital stock at the Rk t rate to intermediate goods producers. Households can raise capital in two ways.

− Through increasing investment, I_t, which leads to an increase in capital stock.

− Changes in the amount of capital utilization.

We assume that the process of capital accumulation is carried out using Eq. (8).

It

kt = (1 − δ)kt−1 + [1 − s ( )] It, (8)

It−1

where δ is the depreciation rate of investment, It i is the gross investment of the private sector, and S(0) is the investment cost adjustment function, which is a positive function of investment changes. S(0) represents the resources lost to transform the new investment into capital stock.

In the case of a static equilibrium where z = 1, S′(1) = S(1) = 0 and S′′ > 0, so the adjustment cost depends only on the second derivative.

According to the above, the household problem is maximizing the utility function relative to the budget. In the optimization process, households choose the amount of consumption, deposit, labor supply, capital stock, investment, and utilization of capital in a way that maximizes their objective function relative to the budget:

c,t 1−σm 1−σ 1+η M

(Cj−bC ) (Nj) ( tc ) i c,i j j ∞ t t−1 t Pt d bt−1 mt−1 WtNt

Max Et ∑t=0 {[ − + ] + λt [(1 + rt−1) c + c + + +

1−σ 1+η 1−σm πt πt Pt

[Rk t ut − Ψ(ut)]Kj t−1 + TRit − Tti + Divt i − ct i − It i − bi t − mc t,i] + Qt [(1 − δ)kt−1 + [1 − (9)

It

S (I )] It − kt]} , where λt is the coefficient of the process related to the budget constraint, and Qt is the coefficient of the process related to capital stock. The first-order condition for each period t≥0 is as follows1:

(∂ct)(ct − bct−1)−σ = λt. (10)

(∂It)Qt [1 − S ( It ) − S′ ( It ) . It ] + βEtQt+1S′ (It+1) (It+1) = λt. (11)

It−1 It−1 It−1 It It

(∂zt)Rk t = Ψ′(ut). (12)

(∂Kt)Qt = βEtλt+1[ut+1Rk t+1 − Ψ(ut+1)] + β(1 − δ)EtQt+1. (13)

(∂bt)Qt = βEtλt+1(1 + rt ) c = λt. (14)

πt+1 c c −σ 1

(∂mt )(mt ) m = λt − βEtλt+1 c . (15)

πt+1 η Wt

(∂Nt) − Nt + λt c = 0. (16)

Pt

For modeling the wage adjustment process, similar to the studies conducted by Kollman [10] and Erceg et al. [11], it is assumed that households in the labor market determine their wages because they offer their labor force under exclusive competition conditions. However, it is not always possible for them to adjust their wages optimally at any given time. The probability that a representative household can adjust its nominal wage optimally is equal to 1-θw. On the other hand, households who do not have the opportunity to adjust their wages accordingly are expected to index their wages relative to past prices based on Relation 24:

Wtj+1 = (∆pt)ωwWtj, (24)

where ωw is the degree of wage indexation. When ωw = 0, there is no wage indexation. However, in the case of ωw=1, complete indexation is performed. The percentage of households who do not have the opportunity to adjust their wages, according to Relation (24), will measure their wages so that in the future, an opportunity will be found to adjust optimally. Given this limitation, when households adjust their wages optimally, they are not likely to adjust them for many future periods for θw.

The problem that households are looking for is actually solving a part of the Lagrange equation Function (9) with respect to the implications in the demand equation for labor Eq. (3) and it is wage indexation relation Eq. (24), that is, Eq. (25). can be used to write the marginal Tobin Q relation, which derives from the ratio can be used to write the marginal Tobin Q relation, which derives from the ratio:

j j j

(Nt) (∆pt+s−1)ωw W N

max E ∑∞ k=0(βθw)k [− + λt+k ∏k s=1 t t],

j 1+η (∆pt+s) Pt Wt

(25)

j −ϕ j k ω Wt

s. t: Nt+k = [∏s=1(∆pt+s−1) w ] Nt+k for all k ≥ 0.

Wt+k

By replacing the demand curve for labor in the target function and after performing the required algebra operation, the first-order condition of the nominal wage would be equal to Eq. (26).

̅ W ̅̅ ∆p ωw (1+ϕ)(Nj Uc t+k) j

t E ∑∞ k=0 βkθk w ( t ) t+k = E ∑∞ k=0 βkθk wN Ut N +k, (26)

Pt ∆pt+k ϕ t+k where, Ut N +k is the ultimate cost (Non-utility) caused by labor supply and Ut c+kU is the marginal utility of consumption. Eq. (25) suggests that the nominal wage at time t for the ith household, which provides the adjustment opportunity, will adjust it so that the present value of the resulting return on labor is equal to a markup value on the present value of the marginal cost arising from work (Ultimate inappropriateness)1. When wages are quite flexible (i.e., θw = 0), the real wage is equal to the markup value (1+φ)/φ of the marginal labor cost ratio (the lack of marginal labor utilization) to the marginal utilization of consumption in the current time. Under these conditions, the real wage dynamics are determined using the process presented in Eq. (16). This means that households supply their labor force in perfectly competitive conditions, and wages are flexibly adjusted in a fully competitive market.

But in monopolistic competition conditions, as stated, in each period, 1-θw% of households succeed in adjusting their wages at an optimal level ̅W ̅̅̅t, and θw of the remaining percent partially index their wages with the inflation rate; thus, using Eq. (3), the total wage index can be written as Eq. (27).

Wt1−ϕ = θw[Wt−1(∆pt−1)ωw]1−ϕ + (1 − θw)(W ̅t)1−ϕ. (27)

Another issue faced by Intermediate goods producers is price adjustments. In this study, the Calvo method [12] was used to adjust the prices. That is, in each period, only (1-θp)% of them will be able to optimize their product prices optimally; other firms (θp%) that cannot determine prices optimally in the current period, based on past prices using Eq. (28) partially indexes prices.

Pti+1 = (∆pt)ωPPti, (28)

where Δpt represents the inflation rate, and ωp∈(0.1) is the parameter that shows the degree of price indexation. In each period, the goal of domestic production companies is to maximize the present value of the expected future profit for future periods in terms of the demand function for the product made by the marginal producers, that is, Relation (29).

∞ k λt+k k ω Pi t i

max E ∑k=0(βθP) [∏s=1(∆pt+s−1) P − mct+k] Yt+k.

Pi λt Pt+k

(29)

i −λt i k ω Pt

s. t: Yt+k = [∏s=1(∆pt+s−1) P ] Yt+k for all k ≥ 0.

Pt+k

By replacing the demand curve in the objective function and deriving from the recent relation concerning the firm's optimum price (̅ Pt), the first-order condition for the firm's problem will be as Eq. (30).

∞ k k ω λt P ̅t ∞ k

E ∑k=0(βθP) λt+k. λt[∏s=1(∆pt+s−1) P] Yt+k = E ∑k=0(βθP) λt+k. (1 −

As a monetary authority, the central bank can set the rate of bank deposition rt d. Accordingly, in modeling the behavior of the central bank, it is assumed that the monetary authority in setting the policy rate follows the Taylor rule. In this rule, monetary policy is determined through the interest rate reflection law, and in fact, it is a response to the deviation from the rate of bank deposits and some economic indicators in a stable situation.

rt d = ρrrt d + (1 − ρr)γp∆pt + (1 − ρr)γyyt + (1 − ρr)γμμt + εz t (32)

In Eq. (32), μt is the rate of money growth in the economy.

Now, the growth rate of money in period t is defined as Eq. (33):

Mt mt∆pt

μt = M = m . (33)

t−1 t−1

γp > 1 and γy > 0 , γμ > 0 are shown as the weighted parameters of inflation, the rate of growth of money and production variables in the monetary policy, and also the long-term response of the bank deposits to these variables. The shock εz t is due to the central bank's policymaker's mistake in determining the interest rate (Profit) of the target. As can be seen, this type of shock directly enters the monetary policy principle and, as an exogenous and random variable, affects the variable of interest rate on the investment deposit.

According to Saxegaard et al. [13] and Agénor and Montiel [14], it is assumed that the interest rates on loans granted by banks to firms (rt l) are equal to markup (μ), as well as the interest rate on bank deposits (rt d).

Mt mt∆pt μt = = . (34) Mt−1 mt−1

In Eq. (34), ul t is the momentum of the interest rate (Interest) of the bank loans and as ul t~N(0, σ2 l ).

Market liquidation conditions require that in all inputs, intermediate and marginal goods are equal to demand. The economic resource constraint is in the form of Eq. (35).

Y = Ct + It + Gt + Ψ(ut)kt−1. (35)

In this section, the model parameters are adjusted based on research on the Iranian economy and typical values in the academic literature Table 1.

1 Since some of the parameters used in this model have been evaluate them, and only they are used by referring to estimated by other researchers in their studies; and their references.

values are not changing over time, there is no need to re-

Based on the results obtained, the conventional method in RBC models is used to evaluate how well the pattern can be explained. The sample includes yearly data from 1982 to 2022. The data in this study are based on constant 2016 prices and are segmented into populations to calculate per capita income. Following logging, they were de-processed using the Hedrick-Prescott filter (λ=100). Table 2 presents a comparison between the autocorrelation and standard deviation of the actual variables during periods of zero gaps and their simulation values derived from the new Keynesian model. According to this table, the model replicated the values of the variables mentioned above. The actual autocorrelation coefficients at intervals 1 and 2 for real production without oil are 0.96 and 0.21, which closely match the simulated values of 0.58 and 0.20. The standard deviation of the real data was 0.046, whereas the estimated value closely approximated 0.039. The impact on actual consumption was deemed to be satisfactory. Basically, the Autocorrelation coefficient values for real consumption in intervals 1 and 2 are 0.65 and 0.12, while the simulation values are 0.55 and 0.26, showing a high level of similarity. The deviation between the actual data and the estimated value was 0.046 and 0.048, respectively, with all other variables remaining constant.

Here, we present the outcomes of the computations and instantaneous reaction graphs for different economic factors. It involves using the linear equations provided in the appendix to analyze and interpret the impacts of technological impulses, price markup, and tightening monetary policy (Raising the interest rate for firms) on the variables being studied in the presence of a cost channel in monetary policy.

Due to a 2% increase in productivity spurred by improved production factors, manufacturing firms will require higher levels of capital and labor, leading to increased investments and production in the economy. An uptick in the need for resources results in higher production inputs such as actual salaries and actual interest rates. This leads to higher household income through increased capital rent and wages, leading to an increase in the consumption of goods and services in the economy. Increasing levels of consumption and investment will result in an increase in the overall demand within the economy. Simultaneously, as the total supply in the economy rises due to the increased productivity of production factors, there is not enough surplus demand, leading to a decrease in inflation levels. Fig. 1 displays the impact of productivity shocks on total consumption variables (c), production (y), real wage (w), and inflation rate (pi) in accordance with the

Fig. 2 compares the immediate response functions of the six production, investment, consumption, inflation, wages, and employment variables in the simulation of price markup impulse. A 5% price mark-up shock caused a 4.5% decrease in production at the start of the survey period. However, the production gradually increased and reached zero by the fourth quarter. At the start of the period, the impact of momentum on investment was approximately -0.2% and increased gradually. Inflation is positively affected by this impulse, resulting in an 80% increase in inflation. However, after two periods, the impulse effect dissipates, and inflation stabilizes. The impact of impulse on consumption starts at around -1.8 at the start of the period and then increases over time before declining in the fourth period.

Fig. 3 compares the impulse response functions of six production-related variables (Production, investment, consumption, inflation, rent of capital rate, employment) with a cost channel of 0.5 (Black lines) and a cost channel of 0.1 (Blue lines) when simulating the impact of interest rate impulses on bank facilities for firms (1%), which essentially tightens monetary policy. If the cost of the channel is low, this model will consistently display a lower response rate following a tightening of monetary policy compared with when the channel cost parameter is higher. Inflation is influenced by the real cost of production, which is determined by both the wage and rental rate of capital due to Calvo's pricing. Both factors consistently declined following the implementation of a restrictive monetary policy. To demonstrate the inflation-boosting model, it is crucial that the nominal interest rate positively affects the ultimate cost. This is accomplished by adding the cost channel of the monetary policy, causing the nominal interest rate to become part of the total cost.

An increase in inflation is caused by a more substantial tightening of monetary policy, with the rate of inflation increasing further if the cost channel parameter is higher. For example, when γ=0.5 and γ=0.1, a 1% increase in the interest rate leads to a 4% and 1% inflationary rise, respectively. The speed of the production reaction remained constant. The impact on consumption starts negative, but as time goes on, it increases and becomes stronger in the model owing to the higher cost channel parameter value. The impact of this sudden push on job opportunities is adverse, and it will become nonexistent starting from the fourth period. In the model, the effect of this impulse on investment is initially negative and remains negative after ten periods.