A Mathematical Model and Programme Support for Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

This paper studies the problem of interdependence between central bank and commercial bank goals. The basic central bank task is to achieve and to maintain price stability. Croatian external debt has been increasing for years and so the activities of the Croatian National Bank are designed to correct this situation. In order to stop the further increase of the external debt, the Croatian National Bank uses several monetary policy instruments, among which is the marginal reserve requirement. On the other hand, the goal of commercial banks is to maximise profits. Banks take loans from abroad at a lower interest rate and invest this money in Croatia at a higher interest rate, thus fulfilling their goal. In order to obtain the desired effects of the marginal reserve requirement, its optimal percentage value should be determined. This problem is modelled as a bi-level mixed 0-1 programming problem. The objective of the leader (Croatian National Bank) is to minimize the increase in household loans by setting different percentages of the reserve requirements for loans extended to households and for those granted to enterprises. The objective of the followers (banks) is to maximize profits. In order to solve this NP-hard problem a heuristic is proposed. In order to verify the model, the paper ends with simulations and the presentation of computational results.monetary policy instruments, commercial banks credit activity, marginal reserve requirement, bi-level mixed 0-1 programming problem, NP-hard problem, heuristic

A Mathematical Model and Programme Support for Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

This paper studies the problem of interdependence between central bank and commercial bank goals. The basic central bank task is to achieve and to maintain price stability. Croatian external debt has been increasing for years and so the activities of the Croatian National Bank are designed to correct this situation. In order to stop the further increase of the external debt, the Croatian National Bank uses several monetary policy instruments, among which is the marginal reserve requirement. On the other hand, the goal of commercial banks is to maximise profits. Banks take loans from abroad at a lower interest rate and invest this money in Croatia at a higher interest rate, thus fulfilling their goal. In order to obtain the desired effects of the marginal reserve requirement, its optimal percentage value should be determined. This problem is modelled as a bi-level mixed 0-1 programming problem. The objective of the leader (Croatian National Bank) is to minimize the increase in household loans by setting different percentages of the reserve requirements for loans extended to households and for those granted to enterprises. The objective of the followers (banks) is to maximize profits. In order to solve this NP-hard problem a heuristic is proposed. In order to verify the model, the paper ends with simulations and the presentation of computational results

Matematički model i programska podrška za određivanje vrijednosti granične obvezne pričuve kao instrumenta monetarne politike

U radu se promatra problem međuovisnosti ciljeva središnje banke i poslovnih banaka. Osnovni je cilj Hrvatske narodne banke postizanje i održavanje stabilnosti cijena. Zbog višegodišnjeg problema visokog udjela inozemnog duga u BDP-u, aktivnosti središnje banke uvelike su usmjerene na destimuliranje rasta zaduživanja poslovnih banaka u inozemstvu. Radi sprječavanja daljnjeg rasta inozemnog duga poslovnih banaka, HNB se koristi s nekoliko instrumenata monetarne politike, među kojima se posebno izdvaja granična obvezna pričuva. Nasuprot tome, cilj poslovnih banaka je ostvarenje što veće dobiti. Pritom se one zadužuju u inozemstvu po nižoj, a sredstva plasiraju u obliku kredita na domaćem tržištu po višoj kamatnoj stopi i tako ostvaruju svoj cilj. Da bi granična obvezna pričuva imala željene učinke, potrebno je odrediti optimalni postotak izdvajanja. Za to je razvijen matematički model dvorazinskoga mješovitog 0-1 programiranja. Cilj voditelja (u ovom primjeru HNB-a) jest određivanjem različitih postotaka pričuve minimizirati porast kreditnih plasmana stanovništvu od poslovnih banaka, a cilj sljedbenika (poslovnih banaka) jest maksimizacija dobiti. S matematičke je strane to NP-težak problem i stoga se za njegovo rješavanje primjenjuje heuristika. Na kraju su provedene simulacije radi verifikacije modela i izloženi rezultati numeričkih izračuna

THREE-DIMENSIONAL PRINTING OF THE ZAGREB UNIVERSITY OF APPLIED SCIENCES LOGOTYPE FROM CHOCOLATE

Trodimenzionalni ispis razvio se iz želje za brzim kreiranjem vlastitog prototipa u realnom vremenu. Razvojem tehnologije te ljudskom domišljatošću pomiču se granice izrade te se počinju koristiti novi materijali. U radu se objašnjava i prikazuje proces trodimenzionalnog ispisa logotipa Tehničkog veleučilišta u Zagrebu (TVZ) od čokolade kao i kompletan način izrade projekta od njegovih početaka do krajnjih rezultata. Upotrebom čokolade prikazana je nova vrsta materijala za izradu trodimenzionalnog ispisa te njezine karakteristike u izradi određenog prototipa i određene modifikacije na standardnom trodimenzionalnom pisaču.Three-dimensional printing developed from the desire to create one\u27s own prototype quickly and in real time. As technology and human ingenuity evolve, the boundaries of production are pushed and new materials are used. The paper explains and shows the process of three-dimensional printing of the Zagreb University of Applied Sciences (TVZ) logotype from chocolate, as well as the complete method of creating the project from the beginning to the final result. The use of chocolate demonstrates a novel material for the production of three-dimensional prints and its properties in the production of a particular prototype and certain modifications on a standard three-dimensional printer

A Mathematical Model and Programme Support for Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

This paper studies the problem of interdependence between central bank and commercial bank goals. The basic central bank task is to achieve and to maintain price stability. Croatian external debt has been increasing for years and so the activities of the Croatian National Bank are designed to correct this situation. In order to stop the further increase of the external debt, the Croatian National Bank uses several monetary policy instruments, among which is the marginal reserve requirement. On the other hand, the goal of commercial banks is to maximise profits. Banks take loans from abroad at a lower interest rate and invest this money in Croatia at a higher interest rate, thus fulfilling their goal. In order to obtain the desired effects of the marginal reserve requirement, its optimal percentage value should be determined. This problem is modelled as a bi-level mixed 0-1 programming problem. The objective of the leader (Croatian National Bank) is to minimize the increase in household loans by setting different percentages of the reserve requirements for loans extended to households and for those granted to enterprises. The objective of the followers (banks) is to maximize profits. In order to solve this NP-hard problem a heuristic is proposed. In order to verify the model, the paper ends with simulations and the presentation of computational results

A MATHEMATICAL MODEL AND DECISION SUPPORT SYSTEM FOR DETERMINATION OF THE VALUES OF THE MARGINAL RESERVE REQUIREMENT AS INSTRUMENT OF MONETARY POLICY

Abstract This paper studies the problem of interdependence between central bank and commercial bank goals. The basic central bank task is to achieve and to maintain price stability. Croatian 249-278 (2007) Key words: monetary policy instruments, commercial banks credit activity, marginal reserve requirement, bi-level mixed 0-1 programming problem, NP-hard problem, heuristi