Consider a one-consumer one-firm economy in which u(x) = axz+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.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?
- 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)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 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…
- 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?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 working
- Suppose there are two goods A and B in the economy and these two goods are complementary of each other. At the beginning, the market for each good is in equilibrium. How will an increase in the production costs of B affect both markets? Which properties does the new equilibrium have? Use appropriate diagrams in your ans.Assume that the Demand elasticity of a good is -1 and the Supply elasticity is +2. Assume also that (i) that the price of a complement decreases and therefore Demand shifts out by +2% and (ii) because one of the inputs in production declined in price, the Supply shifts by +2%. In partial equilibrium, the % change in the equilibrium price is -2% -1% 0% 1% 2%Multiple 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.