The consumer's utility function is the following: U=x + 10x0,6 1 The consumer's optimal values of x and x are the given by the following: x 1 2 P 6P 2 +9 P P P 1 1 The compensated demand equations for x and x are the following: x₁=U-10 1 2 6P 0.6 P 2 1 2 1-0.6 1-0.6 x2c Assume the prices are the following: P₁=1, P₂=1, I=10000, and the P₁ that makes x=0 is P₁=16.732. 1 What is the consumer surplus? = - = 6P 1 P 2 6P 1 P 2 1-0.6 1-0.6
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- 21:45 Sat 7 Aug 26% O Screenshot_20210807-213016_Office.jpg 21:30 a) Choose X, and X, to max the utility fxn, U(X,X) =ahX;+(l-a)\n X, st: M = P, X 1 + P,X , a) Consider a price decrease for good 1 from P, toP . Write down the Demand functions for good 1 when prices are P, and when prices drop from PtoP b) What is the compensating income, M° associated with the price change? C) Obtain the SE and IE associated with the price change IIIs the statement true or false? When a demand curve is a downward sloping straight line, the slope of the marginalrevenue curve is twice as steep as the demand curve.19:32 Fri 6 Aug 91% Screenshot_20210806-193021_Office.jpg a) Choose X, and X, to max the utility fxn, UX,„X,)=chX;+(l-a}hX; st: M - P, X + P,X ; a) Write down the demand functions for goods 1 and 2 b) Consider a price decrease for good 1 from P, toP" . Write down the demand functions for good 1 when prices are P, and when prices drop from R toP c) What is the compensating income, M associated with the price change? Obtain the SE and IE associated with the price change 24
- An economist has estimated that the demand function for cars is approximately D = −400P + 4I where I is the mean household income. The Supply of cars is estimated to be S = 2p (a) What is the equilibrium price of cars (it will be a function of I)?(b) How does the equilibrium price of cars change when I changes?If Philip's utility function is U=4 (41) 05+42. 0.5 what are his demand functions for the two goods? Let the price of q, be p,, let the price of q, be p2, and let income be Y. Philip's demand for q, as a function of p, and p, is 91 and his demand for good q, is (Properly format your expressions using the tools in the palette. Hover over tools to see keyboard shortcuts. Eg, a subscript oLet's say that the demand side of the market for Blue Soda is comprised of 3 leading agents/individuals: Anthony, Brad, and Claire. Let P be the price of 1 liter of Blue Soda, and Qd be the quantity demanded of Blue Soda in liters. Here are the key points to the problem: - Anthony buys only one liter of Blue Soda if the price of it falls below his choke price of $10. - Brad's demand for Blue Soda is defined by QdB = 5 - P/2 - Claire buys 2 liters if the price is below $5, 1 liter if the price is between $5 and $10, and nothing if the price is above $10. Using this information, please sketch the individual demands and the market demand by aggregating the three agents/individuals. Label the graph clearly. Please make sure to sketch the individual demands first and then sketch the market demand.
- Consider the movie ticket and popcorn example discussed in Section 17.7. The theater sells two products, tickets and popcorn. Suppose the weekly demand for movie tickets is Quiz = 400-20Ptiz - 10Ppopcorn where Ptix and Ppopcorn are the prices of a ticket and a bag of popcorn, respectively. Suppose that each time a moviegoer buys a ticket, his demand for popcorn is Qpopcorn = 3-0.4Ppo $ where Qd popcorn is the number of bags of popcorn the moviegoer buys. Suppose further that the theater's marginal cost of a ticket is $2, while the marginal cost of popcorn is $1.5. Instructions: Round your answer to 2 decimal places. a. What is the profit-maximizing price of a movie ticket if a bag of popcorn sells for $5 a bag? popcorn 9.75 b. In Section 17.7, the marginal cost of popcorn was $0.50 and the price of a ticket was $8. Explain intuitively why the profit-maximizing price in this problem is different from the profit-maximizing price in Section 17.7. O When the marginal cost of popcorn…A study of a country's colleges and universities resulted in the demand equation q = 20,000 - 2p, where q is the enrollment at a public college or university and p is the average annual tuition (plus fees) it charges.t Officials at Enormous State University have developed a policy whereby the number of students it will accept per year at a tuition level of p dollars is given by g = 7,700 + 0.5p. Find the equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level. What is the total social gain at the equilibrium price? HINT [See Example 3.] equilibrium tuition price p = $ consumers' surplus CS = $ producers' surplus PS = $ total social gain $graph the line of demand and the of line of supply showing point of equilibrium of these two equations: Qsupply = 2.5P + 30Qdemand= -20P + 370
- Suppose we have a market with 200 individuals with preferences over two goods, x and y. 1. Consider that all 200 individuals have the utility function U = x²/3y¹/3 and that each individual has the same income and is subject to the same prices. Calculate the market demand for x as a function of income and prices. 2. Find the own price elasticity of demand for good x. Is the elasticity constant or is it changing at different values of P? 3. Suppose now that we know m = 135, P = 3, 4. What is the market demand for x? This should be a number. and Py 4. Consider now that 100 individuals (type A) have the utility function U = x²/³y¹/³ and the other 100 (type B) have the utility function U = x¹/3y2/3. Each individual still has the same 'y income and is subject to the same prices. Calculate the market demand for x as a function of income and prices. 5. Suppose now that we know m = 250, P = 5, and Py 3. What is the market demand for x? This should be a number. = =Suppose the market demand curve for pizza can be expressed as QD = 100 - 2P + 3Pb, where QD is the quantity of pizza demanded, P is the price of a pizza, and Pb is the price of a burrito. What is the slope of this demand function, and what information does the slope provide?..Suppose that the market for porcelain lupines in Freedonia is perfectly competitive and initially in a long nun equilibrium. Porcelain lupines are normal goods in Freedonia and are produced with a computer aided technology. Porcelain lupines and ceramic roses are substitutes while porcelain lupines and glass vases are complements. Suppose that a government report shows that people who possess ceramic roses are 72.74% more likely to suffer from erectile dysfunction. Describe with the use of diagrams the effects of this report upon the market for porcelain lupines in the short run and in the long run.