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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- Q.4 (a)Define fully a general competitive equilibrium. What are the essential economic and mathematical elements of the proof of the existence of general equilibrium? Enumerate them and explain how an absence of/or any violation in their requirements will affect the outcome in respect of the existence of general equilibrium?5. Consider a two-consumer one-firm economy with a single input good and a single output good. Consumers' utility functions are u4(x4) Suppose that the input good is divisible and that wA = wB = 1/2. Suppose that the output good is indivisible (i.e., that xg, q = 0, 1, 2, ...), and that the firm's production technology is such that it requires 1 unit of input to produce one unit of output. rA + 3r and uB(xB) 4x? + x. (a) Derive the Pareto set of this economy. (b) For all Pareto-efficient allocations from (a), derive a competitive equilibrium for this economy that generates these allocations.Analyse, in two different partial equilibrium models, what the implications of reducing each of these two different forms of food waste would be. Assume perfect competition in both cases. Illustrate your answers graphically. 1) In a rich country, suppose that improved storage technology at the household level means that households can, at no extra cost, reduce their food waste compared to current levels. What will happen to market demand, market supply, and the equilibrium price in the short run as a result? What will the new long run equilibrium look like? 2) In a poor country, suppose that improved storage technology at the producer level means that producers can, at no extra cost, reduce their food waste compared to current levels. What will happen to market demand, market supply, and the equilibrium price in the short run as a result? What will the new long run equilibrium look like?
- Derive a Co 5. Consider a two-consumer economy in which wA = (1,2), wB=(2, 2), u^(x₁,x) = x₁³x₂ and u²(x,x) = x, ³x₂² (a) Illustrate this economy in an Edgeworth box. (b) Derive a competitive equilibrium for this economy. 11_JJ)5. (b) Consider the two-person, two goods economy given by: W₁ = (1/2, 1/2) U₁= 2X11 + X12, U2=X21 + 2X22, W₂ = (1/2, 1/2) (i) Solve for a competitive equilibrium (ii) Show that the MRS of person 1 = MRS of person 2 does not hold at competitive equilibrium. (iii) Is competitive equilibrium Pareto Optimal? Why?iii) Define "Free Good" in a general equilibrium framework. Explain whether the goods are free goods in the following context after determining the equilibrium price. Consider an exchange economy. There are two consumers A and B and two goods X and Y. A has lexicographic preference over good X and B also has the same type of preference. Their endowment is (5,5) each.
- Suppose the production possibility frontier for cheese-burgers (C) and milkshakes (M) is given by C + 2M = 600 a. Show working and graph this frontier. b. Assuming that people prefer to eat two cheeseburgers with every milkshake, how much of each product will be produced? show working and indicate this point on the graph. c. Given that this fast-food economy is operating efficiently, what price ratio (PC/PM) must prevail? show workingAn 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 O For every possible redistribution of goods among the consumers, some of them will be better off and some of them will be worse off. MRT = MRTS for all firms, whether producing good A or good B MRS = MRT MRS = MRTS OPA = MCA and PB = MCB O MUAMYA = MUHao A MRTS = = PA = PA / PB MUAMYA = MCA and MUAmy B = MCB MRT = w/r, where w is wage and r is the price of capital the quantity of one output cannot be increased without decreasing the quantity of the other MRTS between labour and capital is the same for all firms, whether producing good A or good…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…
- A two-good economy is in a competitive equilibrium. The price of a piece of candy is $2 andthe price of a desk is $12. The marginal cost of candy is given by MCc = 2Qc and the marginalcost of a desk is MCd = 4 + 4Qd. The current production level of candy is one piece. What is theoutput of desks? A) Qd = 1B) Qd = 2C) Qd = 4D) Qd = 5Multiple 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.The First Theorem of Welfare Economics (that a competitive equilibrium is Pareto efficient) may not hold for economies with production if Choose one or more: 1)there are decreasing returns to scale. 2)there are increasing returns to scale. 3)there are consumption externalities. 4)all firms act as competitive profit maximizers. 5)there are production externalities.