econ122lec3slides (1)

econ122lec3slides (1) - Econ 122 Lecture 3: Current Account...

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Econ 122 Lecture 3: Current Account Determination in a Production Economy Joel M. David UCLA September 8, 2010 Joel M. David (UCLA) September 8, 2010 1 / 24
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Introduction So far, we have examined an endowment economy without investment and production, so the current account was determined solely by savings. Here, we add a productive sector to the economy, in which &rms invest in physical capital to create output. Otherwise, the economy is almost completely the same as we have seen. How is the current account determined and how does the economy adjust in response to exogenous shocks? Joel M. David (UCLA) September 8, 2010 2 / 24
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Production Technology Consider an economy in which output is produced with physical capital. Denote by K 1 and K 2 the stock of capital at the beginning of each period and assume output is an increasing function of capital, i.e., Q t = F ( K t ) , t = 1 , 2 (1) where Q t is output in period t . F ( & ) is the production function, which is a technological relationship mapping the amount of capital into the amount of output. De&ne the marginal product of capital, which represents the amount by which output increases when the capital stock is increased by 1 unit: MP K = F 0 ( K ) Standard assumptions: F ( 0 ) = 0 , F 0 ( K ) > 0 , F 00 ( K ) < 0. Joel M. David (UCLA) September 8, 2010 3 / 24
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Firms Output is produced by competitive &rms. In period 1, K 1 is predetermined (exogenous) and thus so is Q 1 . To produce in period 2, &rms borrow capital in period 1 at interest rate r 1 . Physical capital depreciates at rate δ between periods 1 and 2. Then the total cost of borrowing one unit of capital in period 1 is r 1 + δ . Pro&ts in period 2 are then Π 2 = F ( K 2 ) & ( r 1 + δ ) K 2 Competitive &rms choose K 2 to maximize pro&ts, taking r 1 as given. The &rst-order condition shows that the the &rm will choose K 2 to satisfy F 0 ( K 2 ) = r 1 + δ , or , MP K = MC K Note that pro&ts in period 1, Π 1 = F ( K 1 ) & ( r 0 + δ ) K 1 are predetermined and totally exogenous. Joel M. David (UCLA) September 8, 2010 4 / 24
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Investment De&ne investment as the new capital stock less the undepreciated portion of the old capital stock: I 1 = K 2 & ( 1 & δ ) K 1 Because K 1 is predetermined, I 1 moves with K 2 . The &rm±s FOC shows that K 2 is decreasing in r 1 and thus so is I 1 . We can graph investment as a function of the interest rate I ( r 1 ) for given values of K 1 and δ : Joel M. David (UCLA) September 8, 2010 5 / 24
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Households HHs are endowed with W 0 units of interest bearing wealth (capital and/or bonds) at the beginning of period 1, which generate r 0 W 0 in income.
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econ122lec3slides (1) - Econ 122 Lecture 3: Current Account...

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