Consider the following exchange economy: u (x1, x2) min {2x1, x2} =(2,2) B = (2,2) u³ (x, x) = min{x, 2x} Let P₁/P2 denote the relative price. Suppose = 1. = (a) Show that both markets clear at this relative price by computing the optimal consumption plan for each consumer and showing that these plans are feasible. (b) What is the associated WEA? How many units are bought and sold on each market? (c) Illustrate this equilibrium in an Edgeworth Box diagram. Your diagram should include the WEA, the budget line, and each con- sumer's indifference curve through the WEA.

Consider the following exchange economy: u (x1, x2) min {2x1, x2} =(2,2) B = (2,2) u³ (x, x) = min{x, 2x} Let P₁/P2 denote the relative price. Suppose = 1. = (a) Show that both markets clear at this relative price by computing the optimal consumption plan for each consumer and showing that these plans are feasible. (b) What is the associated WEA? How many units are bought and sold on each market? (c) Illustrate this equilibrium in an Edgeworth Box diagram. Your diagram should include the WEA, the budget line, and each con- sumer's indifference curve through the WEA.

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section: Chapter Questions

Problem 19SQ

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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.
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The expression, M = PXX+ PYY is called a budget constraint where M = amount of money available for expenditure; PX= price of commodity X; PY= price of commodity Y; PXX= expenditure on commodity X; PYY= expenditure on commodity Y. Use M = PXX+PYY to express Y as a function of X and note that the graph of this function is called a budget line. Algebraically derive: (1) the y-intercept; (2) the x-intercept. State what determines the slope of the budget line. Graph the function for M = 120; PX= 3; PY= 5 andshow what happens to the original budget line if M decreases by 25% with PX, PY constant.
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(2) Graph the following given these two goods and their respective prices: books (units with per week) at price Ph=1; and food (units per week) at price Pƒ= 2: (a) Point A (market basket A) that maximizes satisfaction of a consumer. (b) Point B (market basket B) that is affordable but satisfaction is not maximized. (c) Point C (market basket C) that gives a higher level of satisfaction but not affordable.
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4. The following data pertain to products A and B, both of which are purchased by Jay. Initially, the prices of the products and quantities consumed are: PA = $10; QA = 3; PB = $10; QB = 7 Jay has $100 to spend. After a reduction in price of B, the prices and quantities consumed are: PA = $10; QA = 2:5; PB = $5; QB = 15 Assume that Jay maximizes utility under both price conditions above. Also, note that if after the price reduction enough income were taken away from Jay to put him back on the original indifference curve, he would consume this combination of A and B: QA 1:5; QB = 9 Determine the change in consumption of good B due to the (1) the substitution effect and (2) the income effect using Hicks decomposition.
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ote: - You are attempting cuestios suro 12 Neha and Sonam consume only Coke and Pepsi in a two person and two goods exchange economy. Neha consumes these two goods in fixed proportions such that she consumes 2 bottles of coke with 1 bottle of Pepsi. Sonam's utility function is given by U=4P+BC. In the economy, there is a total of 100 bottles of Pepsi and 200 bottles of Coke. If Neha initially had 60 bottles of Pepsi and 80 bottles of coke, then in the equilibrium position, Sonam will consume: A. between 50 to 60 bottles of Pepsi B. between 52 to 60 bottles of Pepsi C. between 54 to 60 bottles of Pepsi D. between 56 to 60 bottles of Pepsi Answer 04:09 PM 19-10-2021
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