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Chapter-5 - CHAPTER-5 THE BASIC MARKET CLEARING MODEL Three...

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CHAPTER-5: THE BASIC MARKET CLEARING MODEL - Three aggregate consistency conditions must hold: o Since consumption is the only use of output in the model, total production equals total consumption, that is t t C Y = . o Each dollar lent by someone is borrowed by someone else. Hence, the aggregate stock of bonds must equal zero in every period, that is 0 = t B . o Since the stock of money does not change over time, the total that people hold in each period, t M , equals the given quantity, 0 M . - What guarantees the fulfillment of the aggregate consistency conditions in every period? - Interest rate and price level adjusts to ensure that o the total of commodities supplied equals the total demanded. o the total of desired holdings of bonds is zero, and o the total of money demanded equals the aggregate quantity of money. - This is referred to as the general market clearing. - Note that each household regards the interest rate and price level as given. However, the aggregate of households’ choices determine R and P to satisfy the market clearing conditions. WALRAS’ LAW OF MARKETS - Consider the budget constraint of a household. Let s y 1 be the quantity of goods that the household decides to produce and supply to the commodity market during period 1. Likewise, let d c 1 represent the quantity of goods that a household offers to buy or equivalently, demands from the market. Finally let d b 1 and d m 1 be the household’s planned stocks of financial assets for period 1. The budget constraint of the household for period 1 is the following: P m P b c P m P R b y d d d s / / / / ) 1 ( 1 1 1 0 0 1 + + = + + + - Summing up this equation over all households gives: P M P B C P M P R B y d d d s / / / / ) 1 ( 1 1 1 0 0 1 + + = + + + - The capital letters refer to the economy-wide aggregate figures. Given that 0 0 = B , rearranging the terms we have:
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0 ) / / ( ) / ( ) ( 0 1 1 1 1 = - + + - P M P M P B Y C d d s d - The above equation tells us that market clearing conditions are o The total demand for commodities equals the total supply o Any dollar that someone lends corresponds to a dollar that someone else wants to borrow. o People willing to hold the outstanding stock of money. - Note that if two of these three conditions hold then the third condition holds automatically. This is referred to as Walras’ law of markets.
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