= 5. Consider a two-consumer one-firm economy with a single input good and a single output good. Consumers' utility functions are u¹(x4) x + 3x4 and u (x³): 4x² + x. Suppose that the input good is divisible and that wA = wB = 1/2. Suppose that the output good is indivisible (i.e., that xq, 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. = (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. Consider a two-consumer one-firm economy with a single input good and a single output good. Consumers' utility functions are u¹(x4) x + 3x4 and u (x³): 4x² + x. Suppose that the input good is divisible and that wA = wB = 1/2. Suppose that the output good is indivisible (i.e., that xq, 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. = (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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3 Consider a pure exchange economy with 2 consumers and 2 goods. Consumer ? owns 8 units of good 1 and 1 unit of good 2, and his preference is represented by the following utility function: uA(x1, x2) = x1*x2. Consumer ? owns 2 units of good 1 and 4 units of good 2, and his preference is represented by the following utility function: uB(x1,x2)=x1+x2. Assume that the two consumers are allowed and able to trade with each other, and that good 1 is the numeraire. In this case, both consumers act as price-takers. Price takers: a market participant that is not able to dictate the prices in a market. Therefore, a price taker must accept the prevailing market price. Please find the competitive equilibrium of this pure exchange economy.
12. Consider a pure 2-consumer 2-good exchange economy under a competitive price system. Consumers' A and B preferences are represented by utility functions Consider a pure 2-consumer 2-good exchange economy under a competitive price system. Consumers' A and B preferences are represented by utility functions UA(x1A,x2A)=x1A+2x2A, uB(x1B,x2B)=x1Bx2B, and their initial endowments are DA=(2,0) and 2B=(0,2), respectively. Then, a competitive equilibrium allocation is: a) (x1A,x2A)=(0,1), (x1B,x2B)=(1,1) b) (x1A.x2A)=(0,2), (x1B,x2B)=(2,0) c) (x1A,x2A)=(1,1), (x1B,x2B)=(0,1) d) (x1A,x2A)=(1,1), (x1B,x2B)=(2,1) e) none of the previous statements a-d is correct.
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Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…
2. Consider a small island economy where the government is contemplating imposing a tax on bananas to raise revenue for public projects. The islanders' utility from consuming bananas (B) and coconuts (C) is given by the Cobb-Douglas utility function: U(B, C)=B°C1-a where a = 0.3. (a) Write down the consumer's optimization problem and derive the demand functions for bananas and coconuts. (b) Suppose the initial prices are PB $2 and Pc = = $4, and the consumer's income is I = $100. Calculate the initial quantities of bananas and coconuts consumed. (c) Calculate the compensating variation (CV) and equivalent variation (EV) for a tax rate of t = $0.50. Interpret your results in terms of the impact on consumer welfare. (d) Determine the tax revenue per consumer after the tax is imposed, assuming supply is perfectly elastic so the tax falls entirely on consumers. (e) Compare the impacts on consumer welfare between a flat tax equal to the revenue found in part (d) and the per-unit tax.
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