Question

31. Solow model modification. Consider an economy with the production function y = Vk where n=0.03, and 8 =0.07. The only missing part for our model is s which we generally have assumed is fixed and exogenous. i. Calculate the steady state level of capital per effective worker if s = 0.2. k* = It is unrealistic to assume that saving is a fixed percentage of income regardless of the circumstances so let's analyze a model with more complex savings behavior. Suppose c(k) = 0.6 + 0.5vk. (What did we call the 0.5 in this equation in earlier chapters (e.g. Chapter 3]?) ii. If there is no government and the economy is closed the accounting identity for output per worker is that y = c + 1. What is the implied investment function, i(k)? (Work this out and then verify your answer is one of the ones below. Don't look at them hoping it will give you the answer.) a. i(k) = -0.5 + 0.6Vk b.i(k) = 0.5 -0.6Vk c. (k) = 0.6 -0.6Vk d. i(k) = -0.6 +0.5Vk The steady state condition we derived in class was sf (k) = (8 +n + g)k but that assumed a fixed saving rate s. Start from the basic steady state condition Ak = 0 and solve for the non-zero steady state levels (plural, there are two) of capital. (hint: it might help to make a graph to interpret what is going on) iii. the smaller k* = iv. the larger k* = v. You can define the saving rate ass=i/y. Find an expression for the savings rate as a function of k, sk). Does it increase or decrease with k? a. increase b. decrease c. does not vary with k vi. What is the saving rate in the k* from (il)?s = vii. What is the saving rate in the k* from (iv)?s =

This is what I have so far

Answer 1

Y = 5. n=0.03 S= 0.07 &=0.2. At steady state sy- Chishk. a suk= Cursok a kra nts ON er kete (1) ? - k = ( 0 27 3 10.07) ke-(0.2) [k*=4] clkla ob + 0.55k. os is called MPC : margined propensity to consume y=cal ilks-y-c =4-(0.6 toste] = Tk - 0.6 - vestle Ülk)= o. s k - 0.6 l option (d) is correct li stik) (n+g+5) k. (k)=f(k) & (n+g+S) k. 0.55-0.6 = (0.03 +0.07) k= 0.55 -0.6 - 0.1k. det sk= &k= 22 4 0.53 -0.6 - 0.13 solving: 0.12 ² - 0.53 to 6 = 0. v.lk 3-53+6=0.

3 3² - 33 +23+6=0 7313-3) — 2(3-3) = 0 (-3)(3-2) = 0 Z=3 dez=2. er bolti. bastardo 2-3 k2-3 >> b=3 Z=2 as k²= 2 ) = Smallerke - 2 & larger kr - s . v) $ily e = – 0.6+ 0.55k 19292929297112171799971111111 - - 0.6 +0.5 Ask This ' – Debx (-/2) 0.3 (k)3/2 Tk7312 >o. increase is increases. The option. is because as k increases (a). increases & des also increases. lot of four. please by to Pest sub-parts in Thank you!