Suppose that good 1 is normal and good 2 is inferior. Prove that the total effect on demand for good 1 of a marginal increase in the price of good 2 cannot exceed the total effect on demand for good 2 of a marginal increase in the price of good 1. That is, prove that əx2 др where, for each i = 1,2, zi denotes the Marshallian demand for good i and p; denotes the əx1 дрг
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- This question will let you examine/explore a more interesting utility function than the simple example discussed in class as there will be both cross-price elasticity and an inferior good. Suppose you are told a consumer has the following utility function: U(qx, qz) = qx +√(qx + qz)You should assume income is Y , the price of good x is Px, and the price of good z is Pz. Question:What is the Marshallian demand for goods x and z? I.e. find (qx, qz)for both interior solutions and corner solutions. Note: the outcome is “ugly”for the interior section and both corner should include constraints, i.e. limitsusing Y relative to f(Px, Pz).The demand for Good X in New Bedford, MA is given by the following equation: Qd=60-40P+2I-30Py where: Qd is the quantity demanded of Good X P is the price of Good X I is income Pb is the price of Good Y Assume that the price of Good Y is $6 and income is $700. a. Compute the price elasticity of demand for Good X when the price of Good X is $12. b. Suppose the price of Good X is $12. Using calculus, compute the cross-price elasticity of demand of Good X for Good Y. Explain the meaning of the value you computed. c. Suppose the price of Good X is $12. Using calculus, compute the income elasticty of demand. Explain the meaning of the value you computed.Q1. Assume that the demand curve D(p) given below is the market demand for widgets:Q=D(p)=806−10p, p > 0 Let the market supply of widgets be given by:Q=S(p)=−4+8p , p > 0 where p is the price and Q is the quantity. The functions D(p) and S(p) give the number of widgets demanded and supplied at a given price. What is the equilibrium price? Please round your answer to the nearest hundredth.What is the equilibrium quantity? Please round your answer to the nearest integer.What is the total revenue at equilibrium? Please round your answer to the nearest integer.
- Suppose that the market demand curve for a good is given by D=80-2P-2I, where D is the quantity demanded, P is the price of the good, and I is consumer income in thousands of dollars. The good is a divisible good. The supply curve is given by S = 3P, where S is the quantity supplied. Assume that I = 15. (a) (10 points) How many units of the good are demanded with P = $4? (b) (10 points) Compute the size of a consumer surplus at P = $4. (c) (10 points) Derive the equilibrium price of the good.Assume that the demand curve D(p) given below is the market demand for widgets: Q=D(p)=1651−14pQ=D(p)=1651-14p, p > 0 Let the market supply of widgets be given by: Q=S(p)=−5+10pQ=S(p)=-5+10p, p > 0 where p is the price and Q is the quantity. The functions D(p) and S(p) give the number of widgets demanded and supplied at a given price. What is the equilibrium price? Please round your answer to the nearest hundredth. Answer (1 point) Save your answer What is the equilibrium quantity? Please round your answer to the nearest integer. Answer (1 point) Save your answer What is the consumer surplus at equilibrium? Please round the intercept to the nearest tenth and round your answer to the nearest integer. Answer (1 point) Save your answer What is the producer surplus at equilibrium? Please round the intercept to the nearest tenth and round your answer to the nearest integer. Answer (1…The demand for a good is QA=200+0.3I-PA+2PB, where QA is the quantity demanded of Good A, I is the individual’s income, PA is the price of Good A, and PB is the price of Good B. Which of the following statements is true? a. Good A is a normal Good. In addition, Goods A & B are substitutes. b. Good A is a normal Good. In addition, Goods A & B are complements. c. Good A is an inferior Good. In addition, Goods A & B are substitutes. d. Good A is an inferior Good. In addition, Goods A & B are complements.
- Suppose that the market demand and supply curves for doughnuts (good X) are given by QD = 50 – 40P + 0.03I + 10PY and QS = -150 + 60P – 10W, where P is price of X, I is the average consumer income, PY is the price of cinnamon pretzels (good Y), and W is the wage for workers producing good X. What is the Income elasticity of demand at the market equilibrium? Are doughnuts a normal good or inferior good? Suppose that I = $5,000 and PY = $5. What is the demand curve for good X? Suppose that W = $10 (per hour). What is the supply curve for good X? DO NUMBER 1 !!!!!Q2. Assume that the demand curve D(p) given below is the market demand for widgets:Q=D(p)=1307−11p, p > 0 Let the market supply of widgets be given by:Q=S(p)=−4+8p, p > 0 where p is the price and Q is the quantity. The functions D(p) and S(p) give the number of widgets demanded and supplied at a given price. What is the equilibrium price? Please round your answer to the nearest hundredth.What is the equilibrium quantity? Please round your answer to the nearest integer.What is the consumer surplus at equilibrium? Please round the intercept to the nearest tenth and round your answer to the nearest integer.What is the producer surplus at equilibrium? Please round the intercept to the nearest tenth and round your answer to the nearest integer.What is the unmet demand at equilibrium? Please round your answer to the nearest integer.This problem involves solving demand and supply equations together to determine price and quantity. a. Consider a demand curve of the form QD=-2P+20, where QD is the quantity demanded of a good and P is the price of the good. Graph this demand curve. Also draw a graph of the supply curve Qs =2P-4, where Qs is the quantity supplied. Be sure to put P on the vertical axis and Q on the horizontal axis. Assume that all the Qs and Ps are nonnegative for parts a, b, and c. At what values of P and Q do these curves intersect-that is, where does QD = Qs ? b. Now, suppose at each price that individuals demand four more units of output-that the demand curve shifts to QD - 2P+24. Graph this new demand curve. At what values of P and Q does the new demand curve intersect the old supply curve-that is, where does QD = Qs ? c. Now finally, suppose the supply curve shifts to Q's=2P-8. Graph this new supply curve. At what values of P and Q does QD=Q's? Show all working calculations and label garph with…
- The market for cellular phones has seen a combination of improving telecommunication technology and rising consumer incomes. Suppose you are told that the price of cellular phones decreased over the past five years. The decreasing prices of cellular phones, a normal good, implies that the magnitude of: A. he rightward shift of the demand curve is greater than that of the rightward shift of the supply curve B. The leftward shift of the demand curve is greater than that of the rightward shift of the supply curve C. The rightward shift of the demand curve is less than that of the rightward shift of the supply curve D. The rightward shift of the demand curve is less than that of the leftward shift of the supply curveSuppose that the demand curves for goods A, B, and C have the following functional forms:, where Q denotes quantity demanded and P denotes price: QA = 120 - 3.5 PA + 6PB QB = 100 - 2PB + 3PC QC = 1500 - 0.5PC - 2PA. Based on these demand curves, which of the following pairs of goods are known to be substitutes? Based on these demand curves, which of the following pairs of goods are known to be Complements?The demand for good X is given by Qxd = 6,000 − 1/2 Px − Py + 9 Pz + 1/10 M Research shows that the prices of related goods are given by Py = $6,500 and Pz = $100, while the average income of individuals consuming this product is M = $70,000. a. Indicate whether goods Y and Z are substitutes or complements for good X. b. Is X an inferior or a normal good? c. How many units of good X will be purchased when Px = $5,230? d. Determine the demand function and inverse demand function for good X. Graph the demand curve for good X.