Game theory & Solow Growth Model Practice Problems:

Suppose that there are two countries, Scotland and Canada. Both countries are well- described by the Solow model and have identical Cobb-Douglas production functions: F(K, L) = AKL1-Q The countries have the same level of technology (A) but have different capital to labor ratios, and thus different per capita income. Define the gross return on capital as r, +1 - 6. Let 6 = 0 and o = 1/3 a-) If Canada has 10 times Scotland's per capita income, what is the ratio of per- capita capital in Canada to that in Scotland?b-) If Canada has a 5 percent net return on capital, (and 10 times the per capita income of Scotland), what is the net return on capital in Scotland?Production function is giwn as Leontief: Y = min(AK, BL). Suppose that agents are optimizing. Iniagine that the dynamic system characterizing the solution is as usual under the assumption of zero gmrth rates of population and technology.r - ' 1 naeware and E: Emaaw e 3-) Draw the locus for ll: = 0 on the c In: space [distinguish two regions: is: g; 3,311) b-) Draw f(k) as a function of k. Notice that the derivative f (k) is not defined at k = B/A (to the left of k = B/A we have A, and to the right of k = B/A we have 0), but assume that it is 6 + p. Then draw the locus for c = 0 on the c - k space0-) Draw the direction of r: and it: with wows on the four regions saparated by Kit = D and r} = [l loanses d) Suppose that the steady state occurs where Ii: = and r3 = leeuses intersect with positive level of capital and eensumptien. Disease if there is any idle factor in the economy Consider the Ramsey economy with technological growth, where the consumption and capital law of motions are given by 1 = f ( k ) - e-(nto+x)k and (f' (k) - 6-p-ex) with TVC lim kexp{-[[f'(k) - 6 - n - x]du} =0 1-+00 0 which implies that at the steady state f ( k* ) - 6>n+x. Now assume that the model is on the balanced growth path with steady state values of k* and c. What are the effects of a decline in the depreciation rate, 6, on the k = 0 and e = 0 locuses, and on the k*, c and y*. Explain your results and give a brief economic interpretation