Essay Questions 1. Suppose that the production function (in per capita terms] in a variant of the basic Solow model is given by y = as 5'5 . Capital depreciates at the rate 5=e to and the average saving rate is, s = .20. a. Derive the as equation for this economy algebraically. b. Solve algebraically for steady state levels of k, y, c and i. c. Show the evolution of per capita capital in the Solew diagram. Label steady state levels of k, y, c and i. d. Describe how an economy will evolve if its starting level of capital per capita, k, is below its steady state level of capital per capita. e. New show how dynamics would change on the Solow diagram if saving rate increases to s\2. The Salem-Swan Model a) Consider an economy that is initially in a steady state equilibrium. Assume that in this equilibrium it has a saving rate of 50 per cent and a depreciation rate of 2 per cent. Further assume that the population is constant and that the level of output produced can be represented by the following production function: Y = AKO'L1_\" Where A = 1 and o: = 0.5. Use the Below-Swan model to determine the level of capital per worker and output per worker in this economy. (1 mark) b) Now suppose the government introduces a set of policies to increase domestic savings. As a result, the saving rate increases to 60 per cent. What is the new steady state level of capital per worker and output per worker. (I mark) c) Use a Below-Swan diagram to show the qualitative effects of this increase in total fac- tor productivity upon steady state output per worker and capital per worker. Briey describe the intuition behind this result. (2 marks) d) Economists typically argue that welfare within society is determined by the level of consumption rather than the level of output. How does consumption per worker change in the above example when the saving rate increases from 50 to 60 per cent? Are higher levels of GDP per capita necessarily a sign of higher consumption in the SolowSwan model? (I mark) just dollars instead of thousand dollars (i.,c when income is measured in thousand dollars), what will be the effect on the coefficient for Y and the income elasticity at the market equi- librium, calculated in (c), with other conditions remaining the same? Calculate the income elasticity of demand and explain your results. e) If other things held constant, how would the income elasticity of demand change if the price of pork (p) were reduced to $22? Would the demand be more inelastic with respect to income? f) What is the cross price elasticity with respect to the price of beef (p) and of chicken (p.) at the market equilibrium quantity under the conditions stated above where p = $4 .00 per kg. pr = $3 .00 per kg. Are they Substitutes or Complements? Explain. g) Calculate the clasticity of supply for the following prices by using the supply function above? p = $5, p = $15 , and p =$120 and p + 5co per kg? Note that Q = 100 +6 p - 8 p; where p; = $4.Covid 19 and Economic Growth An economy is characterized by the following production function: f(K, N) = K1/4N3/4. The savings rate in the economy is s=0.3 and the depreciation rate is 6=0.15. 1. a) Derive the per-capita production function. 2. b) Derive the steady state level of capital per worker. How does the capital stock evolve over time if it is at this level? Find the steady state value of output and consumption per worker. 3. c) Read the article "The toll on growth". The author talks about the effect of Covid 19 on economic growth in Africa and mentions, among other things, education. Explain why lower education could lead to lower output and lower economic growth. In the Solow model covered in parts a) - b), would the effect on economic growth be temporary or permanent? 4. d) Assume that educational deficits affect the production function. It is now f(K, N) = 0.8K1/4/3/4. Calculate the new steady state level of output per capita. 5. e) Show graphically the effect of lower education in the Solow model. 6. f) Another channel that the text mentions is government spending. Explain why lower government spending can have a negative effect on economic growth and output. (There is no government in the model, but you can assume that government spending is a type of investment.) Describe how you would model the change in the Solow model. If it helps you, you can draw a Solow diagram