3. Consider a one-consumer one-firm economy in which u(x) = ax2+xq, w = 1 and f(z) = z². (a) Derive a competitive equilibrium for this economy. (b) Derive the Pareto set of this economy.
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- 7. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (a) The conditions require that A and B consume at a point on their budget lines where their indifference curves have the same marginal rate of substitution, and equilibrium for the market as a whole requires that the sum of the individuals' demands for each commodity must equal the totals (Xo and Yo) available. Mathematically express the point of equilibrium, that is, express the above statement with equations in relating each endowments, equilibrium points (Xa, Xb, Ya, Yb), and totals ((Xo, Yo). (b) Suppose MRSa = Ya/Xa, MRSB = Yb/Xb, Xa = 10, Ya, = 100, Xb = 50, Yb = 20, and let good Y be the numeraire (Py =1). Verify that the competitive…a) Suppose demand for good X is given by QD = 900- p/2 where p is the price and QD the quantity demanded. Supply is given by QS = p/4. Suppose 60 TL tax is imposed on each unit ofX that is purchased. What is the burden of the tax? Explain the key factors that determine the incidence of the tax. b) Describe the main differences between partial and general equilibrium analysis in the context of examining tax incidence.An economy with many consumers (Amy, Hao, ...), many producers, two goods (A and B) and two inputs (L and K) is in a competitive general equilibrium. Which of the following conditions are satisfied in this economy? (Select all that apply) The absolute value of the slope of PPF (with good A on the horizontal axis) is equal to MCA / MCB, the ratio of marginal costs of producing goods A and B, at any point on PPF MRSAB = PA / PB for all consumers For every possible redistribution of goods among the consumers, some of them will be better off and some of them will be worse off. MRS = MRT MRS MRTS PA = MCA and PB = MCB MUAmy = MUHao A = PA MRTS = PA / PB MUAmy A = MCA and MUAmy B = MCB MRTS between labour and capital is the same for all firms, whether producing good A or good B. the ratio of input marginal products must be equal to the ratio of input prices MRT = MRTS for all firms, whether producing good A or good B For every possible redistribution of inputs among the firms, the quantity…
- 3. Consider a one-consumer one-firm economy in which u(x) = aTz+1q, w = 1 and f(z) = z2. (a) Derive a competitive equilibrium for this economy. (b) Derive the Pareto set of this economy.3 00:48:16 Graphically, the market demand curve is: Multiple Choice steeper than any individual demand curve which comprises it. the horizontal sum of individual demand curves. greater than the sum of the individual demand curves. the vertical sum of individual demand curvesPlease explain and demonstrate the following questions. Refer to the table below, which shows the maximum number of goods X and Y that producers A and B can produce in one day. Q15. If there are 20 units of good X being produced efficiently each day, how many units of good Y will be produced each day? a) 30 b) 40 c) 50 d) 60 Q16. If there are 20 units of good Y being produced efficiently each day, how many units of good X will be produced each day? a) 40 b) 60 c) 80 d) 100
- 5. Given that excess demands are continuous and satisfy Walras' law, use Brouwer's Fixed Point Theorem to establish the existence of competitive equilibrium in a simple exchange economy. Suppose that an apple orchard is located next to a bee keeper. If the orchard produces x apples and the bee keeper produces y honey and the cost functions of the two are as follows: C(x) = x² + 10x +9 C(y) = y² - 8x What will be the socially optimal amount of apples that can be produced? How does this compare to privately optimal amount?Explain what is a general equilibrium considering Brouwer’s fixed point theoremExercise A.9 In a market only two firms produce a homogeneous good. You work on one of them and are tasked with drawing up the production strategy for the coming year. The two companies in the market have the same information and the objective of both is the maximization of their profit. You know: the inverse market demand curve of the good: P(Q)=200-2Q where Q = q₁ + q₂ , the function that represents the costs of your company and the rival company: C(qᵢ) = 20qᵢ (for i=1, 2), and the data in the following table, with the optimal decisions according to the different types of competition:C(qᵢ) = 20qᵢ and the data in the following table, with the optimal decisions according to the different types of competition: q1 q2 P Bertrand 45 45 20 Cournot 30 30 80 Collusion 22,5 22,5 110 a) What is more in your company's interest to compete or cooperate with the rival company? Keep in mind that explicit collusion agreements are illegal, so each…
- True/False For each of the following, you MUST indicate whether the statement is TRUE or FALSE and you MUST explain why. 1. 2. 3. 4. 5. A Nash Equilibrium is always Pareto Efficient. When there is production, a Competitive Equilibrium is not always Pareto Efficient due to possible increasing returns to scale. A Prisoner's Dilemma must involve prisoners. This is what makes the model interesting. A Pigouvian Tax to correct for the inefficiencies caused by a negative externality should be corrected by placing the tax between the Private Demand and the Social Demand at the intersection of Supply and Private Demand. To find the Social Welfare Function, simply add up the individual utility functions of each member of society.P(Q) (or MSB) = 50 - 0.5Q Р(О) (MPC) %3 25 + 0.5Q МЕС - 0.5Q Рс (Соmpetitive Equilibrium Price) %3 37.50 Qc (Competitive Equilibrium Quantity) = 25 Pe (Efficient Equilibrium Price) = 41.67 Qe (Efficient Equilibrium Quantity) = 16.66 1) Sketch the curves for these functions and illustrate the competitive equilibrium and label Pc and Qc and efficient equilibrium (labelling Pɛ and QE). 2) On the diagram from part 1, illustrate the areas that correspond to the loss in profit for the firm, the total gain to society and the net gain to society when comparing the competitive equilibrium to the efficient equilibriumMultiple choice question. As opposed to general equilibrium analysis, partial equilibrium analysis looksa) at an equilibrium and changes to it in a single, isolated market.b) at how changes in all other markets effect a particular market.c) at how equilibrium is determined in all markets simultaneously.d) at either price or quantity movements.