Which of the following expressions illustrates the point that lifetime consumption (over a two-period framework) should equal lifetime earnings? Assume that the rate of interest is zero. C denotes consumption, W denotes wages, H denotes hours, I denotes leisure, and the subscript denotes the periods. OC1 C2 =W₁H 1 + W 2H 2 OC1 C2 =W₁ (H 1 + H₂) OC₁+C2=W₁H ₁ + W 2H 2 C₁ + W₁H₁ = C2 + W 2H 2 *
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- 4. Given the utility function U(C₁, dt+1) = Inc, + Blndt+1 and the production function F(K,L) = K*L¹-* where c, is the consumption of the young and dt+1 is the consumption of the old. The growth rate of population is given as Nt+1 = (1 + n)N₁ The constraints are given as follows: Ct + St = Wt dt+1 = Rt+1. St Find the steady-state values of per capita physical capital, saving and consumption.3 Assume a closed economy, perfectly elastic labor supply, and linear technology. Suppose the incremental capital-output ratio (ICOR) is 3, the depreciation rate is 3%, and the gross savings rate is 10%. Use the Harrod-Domar growth equation to determine the rate of growth. What would the gross savings rate have to be to achieve 5% growth? Assuming a perfectly elastic labour supply, state one criticism of this model from an exogenous growth theory viewpoint and another criticism of this model from an endogenous growth theory viewpoint.Consider the simple (one-period) production model. The production function is Cobb-Douglas, exhibits constant returns to scale, and the exponent on capital equals 0.25. In year 2010, the economy's parameter values were A=50, K=600 and L=600? Compute the equilibrium wage. Pick the closest value. None of the other options Between 7 and 8 Between 15 and 18 Between 2.3 and 6.8 Between 12 and 13 Over the following decade, the economy experienced several flooding events that destroyed capital but, thankfully, did not kill people. As a result, in year 2020, the stock of capital has fallen to 300 (but the workforce remains unchanged). Compute the equilibrium wage in year 2020. Pick the closest value. Between 15 and 18 None of the other options Between 2.3 and 6.8 Between 12 and 13 Retween 7and 8
- 1. Why is the interest rate irrelevant in the one-period general equilibrium model? What is the mechanism for the interest rate affecting labour supply in the two period model?QUESTION 18 The table below represents national macroeconomic data for Year 1 and Year 2. Year Y K N 1 3200 1800 2 3200 1800 ? Suppose that the production function is given by y=AK0.3y0.7. Between Year 1 and Year 2, the total factor productivity of this economy changed by 7.9%. Given that information, how much did N change in percent terms approximately? (Submit your answer with up to two decimals, i.e., -10.22 for -10.22% and 11.44 for 11.442%.)Do you agree that capital is topmost factor under the category of resources? Why? Please explain and justify your answers. When it comes to knowledge on customers' needs and expectations, does the three variables such as observations, interviews, and market research are really factors in product development? Why? Kindly elaborate your answers per variable.
- Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zND where Y is the output of the con- sumption good, z is the exogenous total factor productivity, ND is the labour hours. Government has to finance its expenditures, G, using a lump-sum tax, T, on the rep- resentative consumer. There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U (c, l) = α ln c + (1 − α) ln l (1) where 0 < α < 1 is a parameter. Answers for part b below: A consumer's choice of optimizing its consumption and labor hours (h - l ) is given by the point where , MRS(c , l) = wage rate Now , MRS (c, l) = MU(c) /MU(l) MU(c) = dU/d c = a/c MU(l) = dU /dl = (1-a )/l MRS = a (l)1−a (c)a (l)1-a (c) Putting this in optimal condition we have : a (l)(1−a) (c)a (l)(1-a) (c) = w --- (i) l = w…2 5. Consider a one-period closed economy model with government. The aggre- gate production is given by Y = 2N where N represents the employment and z is the total factor productivity. The consumer's preferences are given by U (C, 1) = ln (C) + In (1) subject to the following budget constraint C=w(h-1) +- T where denotes profits. The consumer has h units of time to split between labour supply and leisure. The government spending is denoted by G and lump-sum taxes are denoted by T. The government's budget constraint is G = T. (a) Solve the firm's maximization problem and derive the labour demand curve. (b) Graph the labour demand curve and explain its shape. (c) Show that profits are equal to zero, π = 0. (d) Set up the Lagrangian, solve the consumer's optimization problem and derive the labour supply curve.2 5. Consider a one-period closed economy model with government. The aggre- gate production is given by Y = 2N where N represents the employment and z is the total factor productivity. The consumer's preferences are given by U (C, 1) = ln (C) + In (1) subject to the following budget constraint C=w(h-1) +- T where denotes profits. The consumer has h units of time to split between labour supply and leisure. The government spending is denoted by G and lump-sum taxes are denoted by T. The government's budget constraint is G = T. (d) Set up the Lagrangian, solve the consumer's optimization problem and derive the labour supply curve.
- 2 5. Consider a one-period closed economy model with government. The aggre- gate production is given by Y = 2N where N represents the employment and z is the total factor productivity. The consumer's preferences are given by U (C, 1) = ln (C) + In (1) subject to the following budget constraint C=w(h-1) +- T where denotes profits. The consumer has h units of time to split between labour supply and leisure. The government spending is denoted by G and lump-sum taxes are denoted by T. The government's budget constraint is G = T. (g) Derive the equilibrium solution for output, Y*, and consumption, C*, in terms of z, h and G. (h) Suppose that z = 4, h = 24, G = 5. Compute the equilibrium values of N*, w*, Y*, C*, T*. (Hint: You can use the Excel file used in class to verify your answers.) (i) If you use the social planner's problem, would you obtain the same solution? Briefly explain.2. Please go as much as you can to characterize the balanced growth path for the following economy: We introduce leisure into an otherwise standard neoclassical growth framework. Utility function becomes: u(e(t), (1)) = 0)!- –1, (1-((1)) 1-0 where 1-1(t) denotes leisure time and (t) is the time devoted to production. Production function for output is: Y(1) = AK(1)" ((1)L(1))!-a where we also assume population growth rate is n.From what I understand, LBC with work-leisure is c_1 + c_2 / (1+r) = w_1(h-l_1) + w_2(h-l_2) / (1+r). When I manipulate this equation, I get all three of them, which is perplexing since apparently not all of them are correct.