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In short, I'm having problems understanding the LM curve, as the explanation given by the picture is for me, the 4th row is counter intuitive. When risk premium increases it causes the interest rates to go higher, but I don't understand how is it related to the lower demand of money? When there's more demand of money, the interest rates get higher and the curve should shift to the left. Please help.

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When r increases it stimulates savings thus lowers demand for liquidity: LM curve shifts to the right. This lowers nominal exchange rate and through increased net exports stimulates income growth, compensating contraction in investments by greater amount. Here what is important is that although money demand L decreases, it decreases for a given income, whereas in your graph demand L is plotted for each different equilibrium condition of interest rate and income combinations.

As to why the LM curve shifts to the right it has to do with the quantity equation (I love it, pops up almost everywere): Liquidity Demand = (1 / Velocity) x Y. According to this identity a drop in demand, for a given output must be matched by an increased velocity. That means a dollar buys more. If I am correct this must be the reason.

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