ES_Eco202_exam - Eco202 Equation Sheet This study sheet...

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Unformatted text preview: Eco202 Equation Sheet This study sheet includes the part of the course labelled “The Core” in the textbook: The economy in the short, medium and long run. In the past, this material accounted for 50-75 percent of the final exam. Please note that this is study sheet is just a brief summary, and does not replace the textbook in any way. Good luck! ↓ in -- down down ↑ -- right/ down (move along Md) up down ↓ -- left/ up down up spending • Increase in foreign price level a. P* up real exchange rate up (real depreciation) b. e up increases export demand, reduces import demand c. IS and NX-curve shift up Y, i increase d. i up E down (appreciation) (move along UIP) • Increase in expected future exchange rate (Ee up, depreciation) a. UIP-curve shifts up/ right (E has to go up for UIP to hold) b. UIP shift E up e up (real depreciation) c. e up increases export demand, reduces import demand e. IS and NX-curve shift up d. i up E down (appreciation), move along new UIP, but not all the way Increase in money supply a. LM shifts right Y increases, i decreases b. i lower E up (move along UIP), nominal and real depreciation 2. IS-LM IN AN OPEN ECONOMY 1. IS-LM IN A CLOSED ECONOMY • • The IS curve describes a relationship between output and the interest rate; along the IS curve the goods market is in equilibrium. The LM curve also describes a relationship between output and interest rate; along the LM curve the financial market is in equilibrium. • distinguish between domestic demand and demand for domestic goods if demand for domestic goods > domestic demand trade surplus a) with flexible exchange rates • demand in the goods market: Yd = C(Y-T) + I(Y,i) + G + NX(Y,Y*,e) • UIP: i t = it * + For the economy to be in equilibrium both markets have to be simultaneously in equilibrium: Ete+1 − Et Et (b) with fixed exchange rates • fixed exchange rate nominal exchange rate cannot change • i = i*, the domestic interest rate is fixed by the foreign interest rate • money supply has to be such that LM intersects IS at i = i* • no monetary policy possible A mathematical example : Given : C = 100 + 0.6 (Y-T) G = 200, T = 200, I = 100 – 10i (M/P)d = 2Y – 200i ; (M/P)s = 2000/4 = 500 IS: Yd = C+I+G = 280 + 0.6Y – 10i Yd = Y 280 – 10i = 0.4Y Y = 700 – 25i (IS) LM: Ms = Md 2Y – 200i = 500 Y = 250 + 100i (LM) IS = LM 700 – 25i = 250 + 100i i* = 3.6 Y* = 610 POLICY EFFECTS ON IS AND LM: The goods market gives the IS curve and the money market the LM curve. The intersection determines the equilibrium level of output and interest rate. IS LM Output Interest Rate ↑ left/ down (reduction in demand) -- down in taxes right/ up -- up ↑ in right/ up (increase in demand) spending • • -- up up Increase in money supply a. LM shifts right i decreases b. i lower E up but E can’t change LM shifts back (MS down), i = i* • Increase in gov’t spending/ reduction in taxes: a. IS shifts up, moving along LM Y, i increase b. i up E down but E can’t change LM shifts right, i = i* c. Y increased “a lot” move along NX, trade balance worsened • Increase in foreign price level a. P* up real exchange rate up (real depreciation) b. e up increases export demand, reduces import demand c. IS and NX-curve shift up d. Rest like increase gov’t spending What happens if up ↓ • Given i* and E the UIP determines the exchange rate E. down in taxes What happens if e Depending on import and export demand net exports may or may not be positive. Policy i up E down (appreciation) (move along UIP) • in money in money I. SHORT RUN • c. left/ down Increase in gov’t spending/ reduction in taxes: a. Demand increases IS shifts up, moving along LM Y, i increase b. i up E down (appreciation) (move along UIP) Increase in foreign income: a. Export demand increases IS and NX-curve shift up b. IS shifts up, moving along LM Y, i increase We’ve helped over 50,000 students get better grades since 1999! Need help for exams? Check out our classroom prep sessions - customized to your exact course - at www.prep101.com II. MEDIUM RUN IN A CLOSED ECONOMY • • The AD curve describes a relationship between output and the price level; along the AD curve the both goods and financial market are in equilibrium. The AS curve describes a relationship between output and the price level; it is derived from the labour market and firms’ price setting behaviour (A) DYNAMICS OF AS-AD WITH FLEXIBLE depreciation and adjustment for growth in the number of effective workers EXCHANGE RATES • Steady State In the steady state output per worker is constant, hence worker per capita must be constant demand for domestic goods = domestic demand – imports + exports ∆k * = sf (k *) − (δ + n + g ) k * = 0 Y = C(Y-T) + I(Y,i) + G + NX(Y,Y*,e) • • • e – real exchange rate = price of foreign goods in domestic goods UIP must hold Changes in p cause a change in the real exchange rate NX curve shifts IS/ AD curves shift Medium run: Y=Ybar, prices adjust change in real exchange rate w ww.prep101.com Key difference to closed economy: Fall in price level causes a depreciation of the real exchange rate (e up) increase demand for domestic goods IS and AD shift right i.e. in the steady state output per effective worker growth is zero, independent of the savings rate Total output grows at rate (n+g): Y = ANy ∆Y/Y = ∆(ANy)/(ANy) = ∆A/A + ∆N/N + ∆y/y = g + n + 0 = (g+n) Output per worker grows at rate g: Y/N = Ay ∆(Y/N)/ (Y/N) = ∆(Ay)/(Ay) = ∆A/A + ∆y/y = g + 0 = g (B) DYNAMICS OF AS-AD WITH FIXED EXCHANGE note: the natural level of output (Ybar) is the point on the AS at P = Pe RATES • • fixed exchange rate implies i = i* money supply/ LM curve determined by IS and i* changes in price level change the real exchange rate 1:1 because the nominal exchange rate cannot adjust What happens if AS Increase in mark-up (1+µ) [i.e. everything that improves firms market power] Increase bargaining power (z up) [or something else that increases z] Increase in structural change [or something else that decreases z] Increase in money supply Increase in gov’t spending AD P Y up -- up down up -- up down • Key difference to closed economy: Interest rate predetermined no independent monetary policy (LM fixed by i* and IS) Fall in price level causes a depreciation of the real exchange rate (e up) increase demand for domestic goods IS and AD shift right IV. THE SOLOW MODEL • down -- down up • • -- up up up -- up up up III. MEDIUM RUN IN AN OPEN ECONOMY The medium run in an open economy differs from the medium run in a closed economy only by the aggregate demand relationship, the supply is unchanged. As in the IS-LM framework the key difference is the distinction between demand for domestic goods and domestic demand. • • Aggregate production function Y = F(K,AN) AN – effective labour or efficiency units Constant returns to scale, decreasing marginal products A grows at rate g, N grows at rate n Output per effective worker Y/AN = y = F(K/AN, 1) = f(k) The Golden Rule • Find the savings rate that maximizes steady state consumption • consumption = output – savings = output – depreciation (in steady state) • maximize distance between f(k) and (δ+n+g)k • find k** such that f’(k**) = δ+n+g Fundamental Solow equation K t +1 = (1 − δ ) K t + sF ( K t , AN ) / AN kt +1 = (1 − δ )kt − ( g + n)kt + sf (kt ) kt +1 − kt = ∆kt = sf (kt ) − (δ + n + g ) kt i.e. the change in per effective worker capital is equal to savings/ investment per effective worker minus To maximize consumption the slopes of the 2 curves need to be equal f’(k) = (δ+n+g) Our Course Booklets - free at prep sessions - are the “Perfect Study Guides.” Need help for exams? Check out our classroom prep sessions - customized to your exact course - at www.prep101.com VI. TWO-PERIOD BORROWING 1. CONSUMPTION CHOICE WITHOUT INVESTMENT 1st period saving/ borrowing = (Y1– C1) 2nd period repayment = (1+ i)*(Y1– C1) w ww.prep101.com 2nd period budget: C2 = Y2 + (1+ i)*(Y1– C1) point A – initial equilibrium/ endowment point B – optimal allocation without investment but international borrowing (part 1) note: current account period 1 = (Y1– C1) [=savings] current account period 2 = i*CA1 + (Y2– C2) [=interest payment + savings] How to solve? 2 conditions: 1. 2. C2 = Y2 + (1+ i)*(Y1– C1) (optimality) C1 = C2 Combine: C1 = Y2 + (1+ i)*(Y1– C1) (1+ i)*Y1] / [2+i] (budget) C1 = [ Y 2 + C1 = C2 , Saving/ Borrowing = (Y1– C1) = [Y1 – Y2] / [2+i] international borrowing makes country better off 2. CONSUMPTION CHOICE WITH INVESTMENT • Closed economy with investment: Invest such that consumption in both periods equal • Marginal product of capital could be very high/ low inefficient • If MP high borrow money this period and pay back next period better off, because return (MP) higher than interest rate • If MP low lend money rather than invest and collect interest payments next period better off, because return on lending (interest rate) higher than on investing (MP) point C – outcome with only domestic investment, marginal product of capital is higher than interest rate (slope production/ investment function steeper than (1+i)) inefficient borrow money to invest until MP = (1+i) point D – optimal investment: marginal product = (1+i) point E – resulting consumption point This economy borrows from abroad to take advantage of domestic investment opportunities economy better off note: current account period 1 = (Y1– C1 – I1) current account period 2 = i*CA1 + (Y2– C2) How to solve? Separation between in investment and consumption decision: 1. Find optimal investment level: MP = (1+i) 2. Use after-investment income and period 1 (=Y1–I1;Y~1 in the graph) and afterinvestment income in period 2 (Y~2 in the graph) and borrow along budget line with slope -(1+i). i.e. use point D, rather than point A, and repeat exercise from part1 Investment and consumption decision are independent! Our Course Booklets - free at prep sessions - are the “Perfect Study Guides.” ...
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This note was uploaded on 04/10/2010 for the course ECO ECO202 taught by Professor Masoudanjamshoa during the Spring '10 term at University of Toronto.

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