The New Trade Theory Part 1 (50 points) (a) Demand Side: Solve the following CES Demand system to get the optimal q (show every step!)

 The New Trade Theory Part 1 (50 points) (a) Demand Side: Solve the following CES Demand system to get the optimal q (show every step!). Exogenous parameters are (price, national GDP, and mark up/ elasticity parameter ): Pi, Y, p = 0; 1; the defined price index (CPI) is: P= 1p!-]1/1-o N 11 U= g IÎ 9711/0, s.t. Σ Piqi = Y i=1 i=1 (b) Production Technology and Economies of Scale. Suppose a cost function is given as: L = 59 + 10, where L is the amount of labor used to produce q. First, back out the production function (q as a function of L). 9 Second, determine if the production function is increasing, decreasing, or constant returns to scale. (c) Productin side: Optimal Pricing Rule. Once the firm knows the demand curve, the firm can start claiming the monopoly power. Suppose the total cost function now defined as: Cost = cqi + f , where c is the variable cost and f is the fixed cost. Utilizing the optimal q, you solved previously, derive the optimal pricing for firms providing product i, solve for pt. And then explain the economic intuition behind the equation (hint: how does the optimal price vary with respect to each right-hand-side parameters). (d) Once you solve for the opitmal pricing for the firm, plug it back to the Price Index to solve for the optimal Price Index. (e) Explain the economic intuition behind the solved optimal Price Index. If the social welfare W = }, how does the welfare (W) increase or decrease as the number of firm N increases or variable cost c increases? Give your intuition on market competition. Who will benefit or lose from import competition? (f) Then use the zero-profit condition (it = 0), to solve for the optimal number of firms N*. (if can't solve this, list what equations you might need from slides in your final answer) (g) Good modeling requires reasonable critiques on previous frameworks. Point one aspect of the Krugman Model you think is not realistic. How you might fix it?