Micros X swatch X Search X sWatc X Q course X Course X C **ON X D2L Assign X PDE Assign X PDE 1402 / X D2L Ch 6 5 X chegg X C 1. A fil X + X C File | C:/Userskemo/Downloads/Assignment%201-Section%20G-January-26-2023-posted%20(1).pdf LG G . . . of 3 Q + Q Page view A Read aloud | T Add text Draw V Highlight v Erase Co Q (30pts) 1. Gardenia is a perfectly competitive economy with K amount of capital and L amount of labour. All factors of production are fixed and fully employed. Technology is described by a Cobb-Douglas production function given by: Y = F(K. D) = (R)" (1) (3) a) For each of the following cases, indicate whether the production function exhibits increasing, decreasing or constant returns to scale. Demonstrate your result (by introducing a "multiple z" of the factors of production) and explain. i) a=0.3, b =0.5 ii) a = 0.4, b= 0.6 iii) a = 0.6, b =0.8 (3) b) If a = 0.3, b = 0.7 and factors of production are paid their marginal products, what is the share of income received by capital and labour, respectively in Gardenia? Show your result and explain. + (18) c) Gardenia recently experienced a devastating tsunami which destroyed 30% of its capital stock, but fortunately, thanks to advance warnings, evacuation efforts were successful, and the labour force has remained unchanged (at its initial level). Assume that in Gardenia output is produced according to the Cobb-Douglas production function given above and that a=0.3 and b=0.7 . (i) What is the percentage change in total output in Gardenia? Explain and draw a graph to illustrate. (ii) What is the percentage change in the real rental rate? Explain and draw a graph to illustrate. (iii) What is the percentage change in the real wage rate. Explain and draw a graph to illustrate. In each case indicate the direction of change (increase or decrease) and derive the percentage change. Show your work. Explain in words. Draw a graph to illustrate the change in each case. (HINT: express the new levels of K and L in terms of the old (i.e., initial) values. For example, KNEW = 0.7KOLD.) 1 28F ENG 20:21 Snow squall Search CMS 02/02/2023 23Micros X Q swatch X Search X sWatc X Q course X Course X C ***ON X D2L Assign X PDE Assign X DDE 1402 / X D2L Ch 6 5 X chegg X C 1. A fil X + X G File | C:/Userskemo/Downloads/Assignment%201-Section%20G-January-26-2023-posted%20(1).pdf LG G . . . 2 of 3 Q + Q Page view A Read aloud | T Add text Draw v Highlight v Erase Co Q (6 pts) (d) Now in a turn of luck, Gardenia was quickly able to restore the capital stock destroyed by the tsunami so that the capital stock has returned to its initial level (its level before the disaster). In addition, Gardenian scientists discovered a cure to a widespread disease. This will permit the Gardenian labour force to be 20% higher. What will happen to the real rental rate in Gardenia as a result of this increase in the labour force? Indicate the direction of change (increase or decrease) and derive the percentage change. Show your work. Explain in words. Draw a graph to illustrate the change. (25pts) 2. Using the long-run model of the economy developed in Chapter 3, illustrate graphically the impact of the alternative fiscal policy measures indicated in parts (a) and (b) below (one graph for each part). Be sure to label: (i) the axes; (ii) the curves; (iii) the initial equilibrium values; (iv) the direction curves shift; and (v) the final equilibrium values. (10) a) Suppose the government decides to reduce the government's budget deficit by increasing taxes. What happens to: (i) national saving; (ii) the real interest rate; (iii) investment; (iv) consumption; and (v) + output? Explain in words why these variables change or why they do not change. Draw a graph to illustrate the impact of this policy on national saving. (10) b) Suppose the government fears a recession and decides to increase both government expenditures and taxes by the same amount (this is a "balanced budget" change). What happens to: (i) national saving; (ii) the real interest rate; (iii) investment; (iv) consumption; and (v) output? Explain in words why these variables change or why they do not change. Draw a graph to illustrate the impact of this policy on national saving. (5) c) Compare the impact on national saving of the two fiscal policy actions (i.e., the one in part 2(a) and the one in part 2(b)). Explain why the change in taxes does not offset the change in government expenditures in part 2(b). (45pts) 3. Consider the following long-run model of an economy: On the supply side, long-run aggregate supply, Y, is produced according to the following technology: Y = A(K) " (I) 1/2 where the technology parameter A= 300, capital K = 9 units and labour Z = 100 units. On the demand side: y = C+I+G and the consumption function and the investment function are given respectively by: C = 300 + 0.75(Y - T) 1 = 1800 - 65r 1000 to 200 1 28F 20:21 Snow squall Search ENG CMS 02/02/2023 23Micros X Q swatch X Search X sWatc X Q course X Course X C ***ON X D2L Assign X PDE Assign X QDE 1402/ X D2L Ch 6 5 X chegg X C 1. A fil X + X C File | C:/Userskemo/Downloads/Assignment%201-Section%20G-January-26-2023-posted%20(1).pdf LG G . . . 3 of 3 Q + Q Page view A Read aloud | T Add text | Draw v Highlight v Erase Co Q C = 300 + 0.75(Y -T) 1 = 1800 - 65r Government expenditures are given by G = 1000, taxes are given by T = 300, and r is the real interest rate. (Here r is measured in percent. In your calculations use the values r = 2.3, r = 3.5 etc., rather than 0.023 and 0.035) Show your work in each part of the question. If necessary, round off numbers to the third digit after the decimal point (For ex. 2.5436 = 2.544) (5pts) (a) Find the value of Y. (10pts) (b)Using the aggregate demand equation and the value of Y you obtained in part 3(a) find the equilibrium interest rate r*. + ECON 2102 G Winter 2023 Professor F. Demers (10pts) (c) What is national saving in this economy? Calculate and explain briefly. (10pts) (d) What is the government budget deficit? Calculate and explain briefly. (10pts) e) Suppose now that the government decides to reduce taxes to T = 200. (i) What is the new equilibrium interest rate r*? Calculate. (ii) What is the new level of national saving? Calculate. (Assume that Y is the same as what you found in part 3(a).) (iii) Draw a graph to illustrate the impact of the decrease in T on national saving and explain briefly in words. Your graph should be drawn with (S, 1) on the horizontal axis and r on the vertical axis (see Chapter 3). You should also indicate the change in the equilibrium due to the decrease in taxes by drawing arrows to show the direction of the shift in the curves.) 1 28F ENG 20:22 Snow squall Search CMS 02/02/2023 23Micros X Q swatch X Search X sWatc X Q course X Course X C ***ON X D2L Assign X PDE Assign X QDE 1402 / X D2L Ch 6 S X chegg X C 1. A fil X + X C File | C:/Userskemo/Downloads/Assignment%201-Section%20G-January-26-2023-posted%20(1).pdf LG G . . . 3 of 3 Q + | CD Page view A Read aloud | T Add text Draw V Highlight v Erase Co Q ECON 2102 G Winter 2023 Professor F. Demers (10pts) (c) What is national saving in this economy? Calculate and explain briefly. (10pts) (d) What is the government budget deficit? Calculate and explain briefly. (10pts) e) Suppose now that the government decides to reduce taxes to T = 200. (i) What is the new equilibrium interest rate r*? Calculate. (ii) What is the new level of national saving? Calculate. (Assume that Y is the same as what you found in part 3(a).) + (iii) Draw a graph to illustrate the impact of the decrease in T on national saving and explain briefly in words. ( Your graph should be drawn with (S, I) on the horizontal axis and r on the vertical axis (see Chapter 3) You should also indicate the change in the equilibrium due to the decrease in taxes by drawing arrows to show the direction of the shift in the curves.) Co3 1 28F Snow squall Search ENG 20:22 CMS 02/02/2023 23