For each of the following, sketch a curve with the appropriate shape given the assumptions: a. An Engel curve for x, where preferences for x and y take a Cobb-Douglas form. b. An Income-Consumption Curve (ICC), if both x and y are normal at lower levels of income, whilst at higher income levels, y is inferior. C. A Price-Consumption Curve (PCC) for y, where the demand for y is perfectly price-inelastic.
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- Suppose that Sam has a utility function u(x, y)= xy2 where x is the amount of good 1 and y is the amount of good 2. The price of good 1 is $10 and price of good 2 is $20, and the income is $ 90. The price of good 1 is denoted by px and the income is donated by m. Derive the equations for income-offer curve, Engel curve for good 1, demand curve for good 1 and solve for the optimal consumption of (x, y).Suppose the demand curves for goods A, B, and C have the following functional forms, where Q denotes quantity demanded, P denotes price, and M denotes income: QA = 120 - 3.5PA - 6PB + 14M QB = 100 - 2PB + 3PC + 1.1M Qc = 1500 -0.5Pc - 300M. Based on these demand curves, which of the following goods are known to be normal goods? A, B and C B A and B only C AEconomics Suppose that an individual receives utility from two goods X and Y and his utility function is given by: u = -1/X –1/Y. a) Derive the Marshallian and Hicksian demand functions for X and Y. b) How would you determine whether X and Y are gross substitutes or gross complements? c) How would you determine whether X and Y are net substitutes or net complements?
- Considering, QDx = - 4Px -0.02R + 2Pz, and assuming that the individual's income (R) is equal to $600, and the price of the good z (Pz) equals $10, if the individual's income (R) reduce to $300, will the individual's demand for good x increase or decrease? CALCULATE and GRAPHICALLY ILLUSTRATE the behavior of demand for good x. Then inform what kind of property this is.Assume the demand for cherries is elastic and that the producer of cherries increases the price of cherries. As a result? A convex indifference curve implies what type of behavior? If a consumer always wishes to consume peanut butter and jam in fixed proportions, he treats these two goods as if they are? Assume PX= $3 and PY = $6 and income = $30. What is the relative price of an additional unit of good X in terms of the amount of good Y that has to be given up? Assume there are only two goods (X and Y). Assume the relative price of good X, is 2 of good Y. If income doubles, the price of X doubles and the price of Y doubles, what will be the relative price of good Y?A). Draw the demand curve with the slope of your choice (individual or market demand). Choose a price level (say, P1) and find the quantity demanded (Q1) for that price, using the demand curve drawn. Now, assume that price increases to P2. What happens to the quantity demanded? How about if we have an increase on the income level? Show what happens and explain. B). Draw the supply curve with the slope of your choice (individual or market demand). Choose a price level (say, P1) and find the quantity supplied (Q1) for that price, using the supply curve drawn. Now, assume that price decreases to P2. What happens to the quantity supplied? How about if we have a decrease in the input prices for that product? Show what happens and explain. C). Draw the supply and demand curves together. Show the equilibrium point. Present graphically the equilibrium price and the equilibrium quantity.
- Consider that there are two goods, good X and good Y, which are perfect substitutes. The consumer has the utility function given by: U(X,Y)= X + aY The prices of the goods are given by px = 3 and py = 6, respectively. The income of the consumer is given by I = 100. a) Choose a value for parameter "a" by yourself. Graphically illustrate the budget line of the consumer and draw some example indifference curves. Then, find the consumption bundle that maximizes the consumer's utility. b) List the possible outcomes for different values of parameter "a".The horizontally oriented definition of DEMAND states that "demand is the quantitites of a good that buyers are willing and able to buy at various prices in a given time interval." Which of the following statements are TRUE? If I really like a good, it does not matter how much I am able to afford to spend on it. The demand for a good is a specific amount. Demand is a behavioral relationship expressing what quantities buyers would want and be able to buy at various prices. If I can't afford to buy a product at today's available prices, I do not have a demand. The demand is all the possible price quantity combinations Demand depends on the availability of supply. Demand is a relationship between price as a variable and quantity demanded as a variable. Demand is a flow and requires a time interval be be fully understood.PLEASE Show ALL Workings and Graphs VERY CLEARLY! Using indifference curve analysis, derive the Hicksian and the Slutsky demand curves for an inferior good and a Giffen good, by clearly explaining what the price elasticity of demand (PED), income elasticity of demand (IED) and cross elasticity of demand (CED) measure in general.
- (In this question we denote income by Y, not by W as in the lecture notes). The following figure shows the consumption of x and y for two market situations. We can conclude that: x is a normal good for all market situations. py is greater than px. It is not conclusive. x is an inferior good for some market situation. y is an inferior good for some market situation.Individual that consumes two goods (X and Y) and has a CES Utility Function of the form: U = 100(X^(0.75) + Y^(0.75)). Income of 1000, the price of Good X is 10 and the Price of Good Y is 20 a) Find the Marginal Rate of Substitution as a function of the quantities consumed of Good X and Good Y. b) Write out the Lagrangian for this problem. c) Solve to find the demand for Good X, the demand for Good Y, and the highest level of utility for this individual. d) Now consider an increase in the price of Good X to 20. What is the demand for Good X and Good Y? What is the Utility of the consumer following the price change? e) Considering the change in demand for each good between parts c) and d), how much is due to the substitution effect and how much is due to the income effect? f) Show your answers on a graph.If the utility function for a consumer is defined by U=6X^0.6Y^0.7 . Given that the consumer's income is 300 currency units and unit price of goods X and Y are 12 and 15 currency units respectively, calculate the equilibrium quantity of both goods. Compute the price elasticity of demand for both goods and interpret your results. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of both goods