Q3 solution needed. another pic is just for helping material 1. Assume that income for household 1 is mi, and let the price of good x be p. Then household l'sproblem ismax 2 In (x1 +) + m, subject to px, + m, s ĩ,Since household 1 will always consume as much as possible to get the most utility, we will havepx, + m, = mg. You can then solve for m, and substitute into the utility function. Then take a first-order condition with respect to x1. Solve for x, to get household 1's demand for good 1.You can solve a similar problem for household 2 and then add the two together to get market demand,2. Each firm needs to produce where MC = price. If you then solve each of these equations for y, andy2. you will have the supply functions for each of the firms. You just add these two together to getmarket supply.Helping material3. These should be pretty straightforward calculations. (Let me know if they don't seem that way!)4. This is going to be a binding price ceiling, so there will be a shortage. Find the quantity supplied byeach firm by substituting a price of 1 into the supply function, and find the quantity demanded by eachhousehold by substituting a price of 1 into the household demand functions. Consumer surplus,producer surplus, and total surplus will be found similarly to #3, except with a different price anddifferent bounds on your integrals. 2. Find the supply function for good 1 of each firm and the market supply function forgood 1, and illustrate each firm supply and the market supply curves in a graphic.3. Find the competitive equilibrium price for good 1, as well as the equilibrium de-mand of each household, the equilibrium supply for each firm, the households' utilityin equilibrium, the firms' equilibrium profits, the consumer surplus, the producersurplus, and the total surplus.4. Suppose that a price ceiling of 1 is put in place. Under the assumption of efficientrationing, find the supply of each firm, the consumption for each household, the newconsumer surplus, the new producer surplus, the new total surplus, and the surplusloss in relation to the competitive outcome.

Solve this question with the help of graph

3. Find the competitive equilibrium price for good 1, as well as the equilibrium de- mand of each household, the equilibrium supply for each firm, the households' utility in equilibrium, the firms' equilibrium profits, the consumer surplus, the producer surplus, and the total surplus.

3. Find the competitive equilibrium price for good 1, as well as the equilibrium de- mand of each household, the equilibrium supply for each firm, the households' utility in equilibrium, the firms' equilibrium profits, the consumer surplus, the producer surplus, and the total surplus.

Microeconomics: Principles & Policy

14th Edition

ISBN:9781337794992

Author:William J. Baumol, Alan S. Blinder, John L. Solow

Publisher:William J. Baumol, Alan S. Blinder, John L. Solow

Chapter5: Consumer Choice: Individual And Market Demand

Section: Chapter Questions

Problem 3DQ

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Khan lives in a world with two consumption goods x and y. Her utility function is U (x, y) = √x² + y². a. If px = $3,py = $4, and her income, I, is equal to $50, what will be the quantities of x and y that Maya should buy to maximize her utility? Make sure that you write out the Lagrangian and the first-order conditions. (Hint: It may be easier to maximize U² than U). Have you found a true maximum? Explain your answer.
There two goods, candy and soda, available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:u(x, y) = −|4 − x| − |4 − y|where x is the quantity of candy (in grams), y is the quantity of soda (inliters), and |.| denotes the absolute value: for any real number r ∈ R, |r| = r if r ≥ 0 −r if r < 0. The consumer has wealth of w > 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Find the demand for candy and soda as a function of wealth w > 0for the following specific prices, explaining how you arrived at youranswers:(i) when p = 1 and q = 2,(ii) when p = 2 and q = 1,(iii) when p = q = 1. For each part (i), (ii) and (iii), illustrate the demand for candy as afunction of wealth in an appropriate diagram
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