Let us consider the following model with increasing returns to scale, where each firm has limited market power, product differentiation is limited and the market share is equal to s<1 (defragmentation effect).In country H, in a given sector, in autarchy, there are n firms that produce the final good employing only labor, whose total supply is equal to L. The wage of workers is normalized to 1. The total cost function to produce q units of the final good is TC = f + c∙q.i) Derive the total labor demand in country H and write the full employment condition in the labor market.

Consider a firm with production function given by 𝑄(𝐾, 𝐸) = 𝐾^1/3𝐸^2/3 K denotes units of capital and E denotes units of labour. Capital is fixed at 27 units. The firm’s output decision has no effect on the price of output or the wage (w). (a) The firm is profit maximizing and can sell output for $12 per unit. Solve for the firm’s labour demand function. That is, express E as a function of w. Note that for this production function, the marginal product of labour (MPL= MP_e) is MP_E = 𝜕Q(𝐾, 𝐸)/𝜕E = 2/3 𝐾^1/3𝐸^−1/3 Show your formulations and derivation.

Consider the following model of the labour market:Labour supply:  =  ×  + Labour demand:  =  − The endogenous variables area)  and b)  and the equilibrium wage, c)  and the equilibrium wage, d) the equilibrium quantity of labor, , and wage, e)  and the equilibrium quantity of labor, 

Assume that a profit-maximizing, perfectly competitive firm hires labor in a perfectly competitive labor market. If the market wage is $12 per hour and the price of the product is $3 per unit, the firm will ahire more workers if each worker can produce 3 units per hour bhire another worker if the output per hour of the additional worker exceeds 4 units chire fewer workers, since the hourly wage exceeds the cost of producing one unit of output dcontinue to operate in the short run but not in the long run

Let us consider the Brander and Krugman (1983) model with imperfect competition. In country H, in a given sector with homogeneous final output, there are two firms: one is domestic and the other is foreign. The marginal cost for production in country H of the domestic firm is c, while the marginal cost for production of the foreign firm is c/τ, where the parameter τ < 1 represents freeness of trade, which is inversely related to the level of trade barriers (transport costs, tariffs, etc.). Let us also recall that, when the domestic firm has market power, the profit maximizing price is p, being equal top = σc/(σ - s)where σ is the market demand elasticity, and s is the market share of the domestic firm in country H.i)       When there is autarchy there are no competitors for the domestic firm in market H. What is the autarchy price, pA, that she charges in this case?

ECON 5118 Assignment 3 The Optimal Growth Model with Labor and Technology Growth Consider an optimal growth model with a production function Yt = Ktα(AtLt)1−α , where Kt is the aggregate capital and Lt is the labor. Capital depreciates at rate 1 and the representative consumer’s preference is given by u(ct) = log ct , where ct is the consumption per capita. The model also includes ˆ National income identity: Yt = Ct + It , where It is the aggregate investment. ˆ Capital accumulation: Kt+1 = It + (1 − δ)Yt , where the depreciation depends on total production now. ˆ Labor dynamics: Lt − Lt−1 Lt−1 = n, where n is the growth rate of population. ˆ Technology dynamics: At − At−1 At−1 = na, where na is the technology growth rate. 1 (1) Please find the expression for the per effective unit of labor form of the production function. (6 points) (2) Please derive the budget constraint for the representative consumer at time t. (6 points) (3) Please write down the maximization problem for the representative consumer. (6 points) (4) Please write down the Lagrangian and derive the first-order conditions. (6 points) (5) Please derive the Euler’s equation and discuss its implication. (6 points) (6) Please find the modified Golden rule. (6 points) (7) Please find the closed form solutions for ˜ct and ˜kt+1. (You may define the relevant parameters by yourself.) (6 points) (8) Please find the endogenous saving rate based on (7). (6 points) (9) Suppose the consumer discounts the future utility at rate 0.74, α is 0.3, and δ = 0.4. The growth rate of technology is 0.02 and the growth rate of labor is 0.02 as well. The economy starts with ˜k0 = 0.001×the last digit of your student ID, A0 = 10×the first digit of your student ID, and L0 = 4. Please show the response function of aggregate output when the consumer gets impatient. You may discuss what impatience means in terms of the changes in the value of the relevant parameter. Please submit your excel file along with your answers. (20 points) (10) Does being impatient affect the endogenous saving rate? Please show it using math or the excel and talk about its economics intuition. (6 points) (11) Does being efficient (a lower δ) affect the endogenous saving rate? Please show it using math or the excel and talk about its economics intuition. (6 points) The Growth Accounting (19 points) Please choose one country and use data to analyze the contribution of different factors (capital, labor, human capital, and one more factor that is relevant in your opinion) to economic growth. Please discuss your assumptions and results. Please submit your excel file along with your answers. [Hint: the recommended the database is the PWT 10.01] 2