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3 The firm's short-run cost-function C,(y,X2) is OAL+X2 OB + 2X2' Ocy. - + 2X2 ODY+ 4X2 4 The long run supply function and the firm's cost function are _ and OA P: 2V2y2 2V/2' OB P. 4V/2 y2. 41/2' OC P: 2V2yz OD P: 4V2 y2. 2 2'2 Suppose a firm's production function is f(x,;x2) = x x2 , the price for output is p; and the prices for the inputs are w, = 1 and w2 = 2. Answer question 2-4: When input 2 is fixed at X2, The short-run factor demand function X, (p,X2) for input 1 is_ and the optimal output is_ O A O B OC Bixzix2 OD 3 The firm's short-run cost-function Cs(y, X2) is OAL+ X2' OB + 2X2' Ocy + 2X2 2 + 4 X2 OD -Suppose a firm has production function f(21, 12) = (min {3x1, 2x2}) /2, and the price of each input is $1. (a) If x2 is fixed in the short run, find the firm's short-run cost function Cs (y, 12). (b) Find the firm's long-run cost function c(y) (c) Find the firm's short-run supply function Ss(p, x2) (d) Find the firm's long-run supply function S(p).Example 5.8.1. Ten years ago a woman aged exactly 35 effected an assurance policy by level annual premiums payable for a maximum of 25 years. The policy provided the following benefits: (i) a whole life assurance benefit of /2,000 payable at the end of the year of death, (ii) a family income benefit of term 25 years, with payments of /300 per month, beginning im- mediately on death, if this occurs within 25 years. The final payment is made in the month ending 25 years after the issue date. Calculate the annual premium on the basis given below: A1967-70 6% interest expenses are 3% of all premiums.Consider market for masks. Not everyone values the mask equally: marginal private benet is 100 Q and marginal private costs are given by 20 (per Q). Given that wearing masks will help reduce spread of virus, marginal benet to others is 1130 = 50 (per Q). o 3.. Draw the marginal private benet (MPB) marginal social benet (MSB), marginal private cost (MPG), and marginal social cost (MSG) curves on a graph. labeling clearly the axes and intercepts. Pay close attention to what is on the Xiaxis and yiaxis. _ ' o b. What is the equilibrium amount of masks? What is the eicient level? 0 c. What is the deadweight loss (D'WL) caused by the externality? Shade in the area. of the DWL on the graph from part (a). What is the welfare gain from moving to the efcient level of Q? o d. For which good is a market absent in this case? Government solution: Suppose the government steps in and decides to correct the externality by subsi dizing masks. o e. Suggest a Pigouvian tax that would induce the efcient consumption. What is the optimal tax rate per unit, and how much subsidy is needed? Market solution: The Cease theorem states that \"the eicient outcome should occur regardless of which party has the property rights,\" implying that the market can potentially solve externalities by itself (no need for the government to step inl). o f. Interpret the Cease theorem in the context of this question. What are ways in which the Cease theorem could fail? Give some examples in the context of this
