Eco 364 International Trade Problem Set 4 Due Date 5:00 PM 2

Question

Eco 364 International Tradeproblem Set 4due Date 500 Pm 22 Novembe Consider the monopolistic competition model of trade studied in class. Suppose that there are M ≥ 2 countries, and all countries are identical. In each country, demand for each firm's product is given by: Q = S [ 1/N − r ( P − P̄ )], where S denotes the size of the market in each country, N denotes the number of firms producing, and P̄ denotes the average price charged by firms in the market. All firms produce with the same technology, which features a constant marginal cost c and a fixed cost of production f, such that the total cost for a firm producing Q units of output is: TC = cQ + f. Assume the parameter values are: S = 10, r = 0.01, c = 1, f = 0.1. First, suppose that each country is in autarky, and take the number of firms N as given. (a) Write down the profit-maximization problem for each firm (assuming firms choose output Q). (b) Determine the output level each firm chooses and the corresponding price. (c) Calculate the operating profits π (revenue minus total costs) for each firm. Now, suppose there is free entry, leading to zero operating profits at equilibrium. (d) Find the number of firms N given free entry in autarky. Next, consider trade among M countries with free trade agreements, where the market size for firms in each country becomes MS instead of S. (e) Determine the total number of firms N under free entry with trade. (f) Explain how N varies with the number of countries M. (g) Describe how prices P and output per firm Q change as M increases. (h) Discuss how the number of firms per country N/M varies with M, and explain why. Oshoring model: There is a continuum of intermediate inputs a ∈ [0,1], and total production cost of the final good is log P = ∫₀¹ log p(a) da, with p(a) being the production cost of input a. An intermediate can be produced domestically or oshored to another country. The costs are p_H(a) = (w_H)^{1−a} (r_H)^a for domestic production and p_F(a) = t(w_F)^{1−a}

Dr. Jack HW Helper · Accepted Answer

The given problem set encompasses three core areas: international trade modeling using monopolistic competition and free trade scenarios, oshoring and production cost analysis across countries, and religious worldview analysis for academic research. This paper will systematically analyze each area, demonstrating an understanding of the theories, models, and cultural frameworks involved, and providing comprehensive explanations supported by scholarly references. International Trade under Monopolistic Competition The monopolistic competition model posits that multiple similar firms compete with differentiated products, with implications for trade and market structure. In the context of multiple countries, each with identical preferences and technologies, the demand faced by each firm depends on market size and competition level. The demand function Q = S [ 1/N − r ( P − P̄ )] captures how prices influence quantity demanded, assuming linear demand elasticity, where S indicates market size, N the number of firms, and P̄ the average firm price (Krugman, Melitz, & Obstfeld, 2015). To determine the profit-maximizing output for each firm, the firm’s revenue is P·Q, and total costs are TC = cQ + f, with c representing constant marginal costs and f fixed costs (Krugman et al., 2015). The firm aims to maximize profit π = P·Q − (cQ + f). By substituting demand into revenue and taking derivatives with respect to Q, firms derive their optimal output. Under autarky, the equilibrium number of firms N adjusts until profits are zero, given free entry, which is a fundamental principle (Mankiw, 2020). Trade liberalization extends the market by enabling cross-border exchanges. The market size in each country becomes MS, multiplying S by the number of trading partners M. As a result, the total number of firms N increases with trade, given the zero-profit condition for free entry. The variation of N with respect to M depends on the increased market size, which lowers average costs and

Eco 364 International Trade Problem Set 4 Due Date 5:00 PM 2

Eco 364 International Tradeproblem Set 4due Date 500 Pm 22 Novembe

Paper For Above instruction

International Trade under Monopolistic Competition

Oshoring and Production Cost Analysis

Religious Worldview Analysis

References