Suppose a consumer's utility function is U(X, Y) = X + 2Y. The consumer has $8 to spend (M = $8)....
Question:
Suppose a consumer's utility function is U(X, Y) = X + 2Y. The consumer has $8 to spend (M = $8). The price of good Y is PY = $2. Fill in the table below which gives price/quantity combinations on the Demand Curve for Good X:
| Px | X |
|---|---|
| 1/4 | |
| 1/2 | |
| 2 | |
| 4 |
Budget Line:
The budget line shows the available resource for any consumer. Thus, it represents the limit of the consumption of any commodity. It is on the consumer how to use this available income for the consumption process.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerAt each price of X, given the income, how much of only X can be bought is calculated below:
{eq}\begin{align*} M &= 8\\ X &=...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
Budget Lines & the Rate of Transformation in Economics
from
Chapter 3 / Lesson 11
8.7K
In economics, the rate of transformation model can be used to visualize the concept of budget constraints. Learn more about budget constraints, budgets lines, the rate of transformation curve, and how to maximize the utility of the concepts.
Related to this Question
- a) Suppose a consumer has a utility function U = x^a y^ (1-a ) , find the consumer demand curves for x ( p , p , I ) and y (p , p , I ) Now , another consumer has utility U = a ln x + (1-a ) ln y ,
- Suppose there are only 3 consumers on a market. Demand function for bread for consumer 1 is Q_1 = 1 - p; for consumer 2 it is Q_2 = 2 p, and for consumer 3 it is Q_3 = 3 p. Find price elasticity of demand at the point on the market demand curve where
- Consider three consumers indexed by i ∈ {1, 2, 3) with the following demand functions for a public good G. p1 = 20 - (1/10) G, p2 = 20 - (1/10) G, p3 = 30 - (2/10) G Where pi is the price consumer i is willing to pay for a quantity of G. If marginal
- A consumer maximizes u(x, y) = xy/2 + 5 given that her income is I, price of x is px and price of y is py. Derive the demand functions of this consumer. (Hint: you may use this fact ax^2 + bx + c = a(x + b/2a )^2 + c - b^2/4a)
- Suppose a consumer's utility function is given by U(x1, x2) = x10.4x20.6. a) What is the consumer's demand for x1 as a function of income and prices? What is the consumer's demand for x2 as a function of income and prices? Use the Lagrangian method or you
- Suppose there are only three consumers on the market. Demand function for bread for consumer 1 is Q_1 = 1 - p; for consumer 2 it is Q_2 = 2 p, and for consumer 3 it is Q_3 = 3 p. Find price elasticity of demand at the point on the market demand curve
- If the consumer's utility function is given by U(x, y) = min(x, y), what is the value of ex,px + ex,py + 7ex,I : ex,px mean elasticity of demand (dgx/dpx )*(px/gx) (a) 0 (b) 6 (c) 1 (d) 9 Explai
- Suppose there are only three consumers on a market. Demand function for bread for consumer 1 is Q_1 = 1 - p; for consumer 2 it is Q_2 = 2 p, and for consumer 3 it is Q_3 = 3 p. Find price elasticity of demand at the point on the market demand curve wh
- Suppose the market demand for good X is given by QXd = 20 - 2PX If the equilibrium price of X is $5 per unit then consumer surplus is A. $100. 2 B. $75. C. $50. D. $25.
- Consider a consumer with utility function given by u(x_1, x_2) = x_1x_2 . (i) Find the demands for goods 1 and 2 when the consumer faces prices p_1 \enspace and \enspace p_2 , and income m . (i
- Consider a consumer with utility function given by u(x_1, x_2) = x_1x_2. A) Find the demands for goods 1 and 2 when the consumer faces prices p_1 and p_2, and income m. B) Are goods 1 and 2 normal goo
- According to the utility model of consumer demand, the demand curve is downward sloping because of the law of: a. consumer equilibrium. b. diminishing marginal utility. c. diminishing consumer equilibrium. d. diminishing utility maximization.
- According to the utility model of consumer demand, the demand curve is downward sloping because of the law of a. diminishing marginal utility. b. diminishing consumer equilibrium. c. consumer equilibrium. d. diminishing utility maximization.
- According to utility model of consumer demand, the demand curve is downward sloping because of the law of a. diminishing marginal utility. b. diminishing consumer equilibrium. c. consumer equilibrium. d. diminishing utility maximization.
- The extended demand function of good X is given by Q_d^X = 1200 - 10P_X + 20P_Y + 0.2M where Q_d^X = quantity demanded of good X, P_X = price of good X, M = average consumer income, P_Y = price of related good Y (related in consumption of X) A. What is Q_
- Suppose that the demand curve is given by D(p) = 10 - p. What is the gross benefit of consuming 5 units of the good? How much money would he be willing to pay to have this amount of consumption rather than nothing at all? If the price changes from $5 to $
- Suppose an agent has preferences represented by the utility function u(x1, x2)=X1 square X2 cube. The price of x1 is 3, the price of x2 is 2, and the income is 10. Mathematically derive this consumer's demand curve for good 1.
- Consider a market with a demand curve of P=42-0.06Q and a supply curve of P=12+0.09Q. Calculate Consumer Surplus.
- A. Fill in the blanks in the table for the market quantity demanded at each price. B. Construct the market demand curve and label it Dm. Suppose there are only three consumers in the market for a particular good. The quantities demanded by each consumer a
- Suppose that the market for good X has only three consumers (1, 2 and 3). Their individual demand curves are given by: Q_1 = 100 - 0.5P Q_2= 150 - P Q_3 = 200 - 2P a) Solve for the market demand c
- Suppose a consumer's preferences can be represented by the utility function: U(X,Y)=X2Y a. Derive the function for the marginal rate of substitution holding utility constant: b. Derive the demand curv
- Consider a market with two consumers, A and B that have individual demand functions of: Q D A = 12 ? 2 p Q D B = 12 ? 2 p and a market supply function of Q s = ? 4 + 2 p a. Plot both demand curve
- Two consumer Exchange economy: Consumer 1 utility u1(x,y)= x^2/3 y^1/3 with endowment e1=(18,7). Consumer 2 utility u2(x,y)= xy with e2=(15,16) a.Compute each consumer's demand ?function for good x a
- Suppose a consumer has 600 dirhams to spend on goods X and Y. the market prices for these goods are P_x = 10 and P_y = 40. A. Write the equation for the consumer budget line. B. Illustrate the consumer's opportunity set C. Show how the consumer's budget s
- The slope of a demand curve describes consumer behavior by showing: a) that the consumer increases his/her consumption of a good when the price goes down b) that suppliers provide more of the good as the pr
- What is the slope of the price consumption curve for two goods, x and y, when preferences are measured by the utility function U(x,y) = x0.5y0.5, the price of good y is $10, income equals $100, and the price of good x increases from $5 to $10? a. slope is
- If the price of good X rises, then the resulting decrease in the consumer's quantity demanded will the consumer's total utility from consuming X and the consumer's marginal utility from that last unit of X consumed.
- Consumer surplus is equal to: a. the area under the demand curve. b. the area under the demand curve above the good's price. c. the area under the demand curve below the good's price.
- The slope of a demand curve describes consumer behavior by showing: a. The consumer increases his/her consumption of a good when the price goes down, b. That suppliers provide more of the good as the price goes up, c. That the consumer increases his/her q
- Suppose there are only three consumers on a market. Demand function for bread for consumer 1 is Q_1 = 1 - p; for consumer 2 it is Q_2 = 2 p, and for consumer 3 it is Q_3 = 3 p. Find the market demand function. Show your work.
- If a demand curve goes through the point P = $6 and Q_d= 400, then: a. 400 units are the most consumers will buy if price is $6, b. $6 is the lowest price consumers can be charged to induce them to buy 400 units, c. $6 is the highest price consumers wil
- Suppose that the demand function for good Y is given as a linear function: Qd(P)=120-2P. where P is the price of good Y. Find the price at which price elasticity of demand for Y is -1.
- If the demand for a product is perfectly elastic, what does the corresponding price-consumption curve (or price offer curve) look like?
- Does a consumer well being vary along a demand curve? a. Yes. When price increases, consumers move to a lower indifference curve. b. Yes. When price increases, consumers move to a higher indifference curve. c. No. When price increases, consumers stay o
- A shift in the consumer's demand for a good X cannot result from a change in the: A) price of a substitute for good X. B) price of X. C) consumer's taste. D) consumer's income.
- The price elasticity of demand may be preferred over the slope of the demand function for measuring consumer sensitivity to changes in the price of a good because the: i. price elasticity is sensitiv
- A consumer's utility function is U(x,y) = y + 54x - 2x^2. Her income is $166. If the price of x is $38 and the price of y is $1, how many units of good y will the consumer demand?
- A consumer must divide $600 between the consumption of product X and product Y. The relevant market prices are P_X = $10 and P_Y = $40. a. Write the equation for the consumer's budget line. b. Show how the consumer's opportunity set changes when the price
- Suppose you have this utility function: u(x1, x2) = x^(1/2)x^(1/2). Prices for good 1 and good 2 are p1 and p2, and income is m. The demand functions are as follows: good 1: x1 = m/2p1 good 2: x2 = m/2p2 If the price per unit for the two goods is p1 = p2
- Consider a situation where a consumer demands two goods, x and z with the utility function: U=x^{0.3}z^{0.7} (a) Derive the marginal rate of substitution (b) Derive the demand functions for x and z a
- Suppose there are only three consumers in the market for a particular good. The quantities demanded by each consumer at each price between $1 and $9 are shown in the below table. ||Price of X||Consumer 1||Consumer 2||Consumer 3||Market Demand |9|0|5|10| |
- Suppose that a consumer's demand curve for a good can be expressed as P= 50 -4Qd. Suppose that the market is initially in equilibrium at a price of $10. What is the consumer surplus at the original eq
- Suppose that the market for a good is composed of 1000 identical consumers. The market demand is given by 150,000 - 25. What is demand for an individual consumer's demand curve? Find the equation and
- For the utility function U(x,y) = 8ln(x) + 2y, with a price of x equal to $1 and a price of y equal to $1, what is the elasticity of the demand for y with respect to income?
- Suppose the utility function is U(x, y) = min(x, y) Determine the substitution and income effect of a change in the price of x, and what is the demand equation for x?
- Which of the following is not held constant along a given demand curve for a good? A. price B. consumer income C. the price of substitutes D. consumer tastes
- Suppose two goods, X and Y, are perfect complements. A consumer has $60 to spend. Initially, the price of each good is $2. If the price of good X falls to $1, how much of the total change in quantity demanded is due to the income effect? Sketch the graph.
- Suppose that a consumer's preferences can be represented by the utility function u(x1, x2) = x1^.6 x2^.4. Suppose that the price of good one, p1, increases. Use calculus to show what will happen to de
- Suppose you have the demand function given: d=40- 2p^2+m, where M is income and P is the price of a good . You have an income of $100. a) Compute the price elasticity of demand. b) If P=1, is the good elastic, inelastic or unit elastic? c) Assuming P=1, c
- Because the marginal utility [{Blank}] with each additional unit consumed, the price of the good must [{Blank}] in order for consumers to buy more of the good. This explains why the demand curve is [{Blank}]. a) Decreases; rise; positively-sloped, b) Inc
- Graphically, consumer surplus is represented by the area: a. below the demand curve. b. above the supply curve and below the demand curve. c. below the demand curve and above the equilibrium price. d. above the supply curve and below the equilibrium
- A consumer has linear demand, x_1 = 10 + 1/10 m - 2p_1. The consumer has an income of $100. p_1 is initially $2. (a) Calculate the gross surplus and consumer (net) surplus at the original price. Interpret these values as if you were explaining it to a no
- Consider a market for air conditioners. Consumers' demand curve for air conditioners is given by Qd = 120 - 3P, while Qs = 30 + 2P (a) Suppose that the price is $40. How much quantity will consumers
- Consumer 1 has demand function q1 = 50 - p1 and consumer 2 has q2 = 50 - 2p2. The per-unit cost of the production is mc = 10. Our conclusion is that if we have only one two-part tariff scheme (f, p)
- Suppose demand and supply are given by Qd = 60 - P and Qs = P - 20. If a price ceiling of $32 is imposed in the market, determine the full economic price paid by the consumers.
- Suppose that the demand function for a good is given by Qd = 30 - P. Suppose that the price of the good is $10. What is the elasticity of demand at that price?
- The following utility functions represent preferences of a consumer over goods x_1, x_2 (and x_3). Prices of these goods are denoted p_1, p_2 (and p_3). Consumer has income m. Derive the demand functi
- Suppose the demand curve for a good is downward sloping and the supply curve is upward sloping. At the market equilibrium, if demand is more elastic than supply in absolute value, a $1 specific tax will: A. raise the price to consumers by 50 cents. B. r
- A consumer faces a utility function defined as U ( X ? Y ? ) and has a budget constraint represented by M = P x X + P y Y . Find the consumers equilibrium
- Suppose the demand function for a product is given by the function: D(q) = -0.014q+65.8 Find the Consumer's surplus corresponding to q = 2,450 units. If necessary, sketch the demand curve, which cros
- Suppose the supply of a good is perfectly elastic at a price of $5. The market demand curve for this good is linear, with zero quantity demanded at a price of $25. Given that the slope of this linear demand curve is -0.25, draw a supply and demand graph t
- Suppose supply of a good is perfectly elastic at a price of $5. The market demand curve for this good is linear, with zero quantity demanded at a price of $25. Given that the slope of this linear demand curve is -0.25, draw a supply and demand graph to il
- The demand curve is downward sloping because of law of a. diminishing marginal utility. b. diminishing consumer equilibrium. c. consumer equilibrium. d. diminishing utility maximization.
- The demand curve is downward sloping because of the law of a. diminishing marginal utility. b. diminishing consumer equilibrium. c. consumer equilibrium. d. diminishing utility maximization.
- You are given the following supply and demand curve functions for a market for sunglasses. Graph the following : Qd= -2 (p)+ 340 Qs = 5P-150 Graph the following: a. The supply curve; b. Consumer
- The demand for a product has been estimated to be Qd = 50 - 2p. Calculate the consumer surplus consumers enjoy from consumption at equilibrium if the current market price is $10. A. $600 B. $450 C. $225 D. $1,350 E. None of the above
- Suppose that the demand curve is given as P+2Q=10 and supply curve is given as Q=2P. At the point of market equilibrium, calculate the consumer surplus.
- Suppose the market demand curve is P = 10 - 2Q. At a price of 6, consumer surplus equals A. 4. B. 8. C. 6. D. 10. E. 12.
- If a firm faces the demand curve P = 60 - Q and the price is $30, the consumer surplus is: a. 200 b. 300 c. 450 d. 650
- Consider the market of paper towels where the supply curve is upward sloping and the demand curve is downward sloping. 1. Suppose there is an effective price ceiling applied on this market. What happens to the consumer surplus as a result? 2. Suppose ther
- Given the Demand and Supply functions: Demand: Qd=2000-12P Supply: Qs=-400+8P a. Draw the demand and supply curve. Identify Consumer and Producer Surplus in the graph. b. Find consumer surplus, produc
- The consumer is said to be at a point of saturation when: A. Marginal utility of a commodity is greater than the price of the commodity. B. The extra amount of money a consumer is willing to pay for an additional consumption equates to the prices of each
- When you look at the demand curve for an individual firm there is no consumer surplus that can be measured because demand is equal to price. Yet, when you look at the market demand situation it is cle
- In the case of a normal good, an increase in consumers' incomes would shift the A. supply and demand curves inward B. demand curve inward C. demand curve outward D. supply curve inward
- The demand curve is given by Q_d = 250 - 2.5P_X - 0.25I - 5P_Y + P_Z where Q_d is the quantity demanded of good X, P_X is the price of good X, I is the consumer income, in thousands, P_Y is the price of good Y, P_Z is the price of good Z A. Based on the d
- Is the downward-sloping demand curve enough to draw inference on the rationality of the consumer?
- Consider the market for a good x. a) Suppose that sons users do not buy any Good x at the price of $130, and for every $10 decrease in price, the quantity consumed increased by 20. Write the equation for the demand curve of good x. b) Suppose that produ
- If a firm faces the demand curve P = 60 ? Q and the price is $30, the consumer surplus is: a. 200 b. 300 c. 450 d. 650 3. If the demand curve is P = 60 ? Q and the supply curve is Q = P, the market
- Considering the demand side of a market for a good, the consumer surplus derived by an individual: i. is the difference between the maximum amount the consumer is willing to pay for each unit and the price he/she actually pays.
- To what extent can indifference curves be used to determine a consumer s demand curve for a product?
- Of the two-price consumption curves shown below, which curve corresponds to a flatter demand curve for good X? Assume that only the price of good X is changing (P_y and income held constant}.
- Provide the: a. inverse demand curve b. consumer surplus c. equilibrium quantity and price Given: Consumer surplus: Qx = 300 - 2Px^4 Price = $30 1. Qx = 300 - Px if Px = $320 2. Qx = 14 - 1/2 Px if
- On a demand and supply diagram, consumer surplus would be the area: a. above the supply curve and below the demand curve up to the equilibrium quantity. b. above the demand curve up to the equilibrium quantity. c. above the market price and below the de
- A consumer has the inverse demand of p = 15 - 2q for a single good. The market price is $6.00. Calculate consumer surplus and the total value of the good for the corresponding quantity consumed. (Ente
- A local store (a monopoly) has two consumers. Consumer 1's demand curve is given by P_{1} = 16 - 0.5Q_{1}. Consumer 2's demand curve is given by P_{2} = 14 - 0.5Q_{2}. The store's total cost curve is
- a) Use the utility function U(X_1,X_2 ) = X_1^(1/2) X_2^(1/3) to get the ordinary demand functions for X_1 and X_2. Given that the budget constraint is M = P_1 X_1 + P_2 X_2, suppose that the consumer
- By drawing a demand curve with price on the vertical axis and quantity on the horizontal axis, economists assume that the most important determinant of the demand for a good is a. consumer income. b
- The demand curve and supply curve for fancy lobster dinners are given respectively as follows: Q_D=150-2P+3M Q_S=3P Where M represents average daily disposable consumer income. Suppose that last year, consumer income was M=$60. Find the equilibrium pr
- The linear demand function, the log-log demand function, and two alternatives forms of the semi-log demand function are simple formulas for demand functions where the quantity of a good demanded is represented as a function of its price and the consumer's
- Suppose the income elasticity of demand for good X is 2, its own price elasticity of demand is -4, its advertising elasticity is 3, and the cross-price elasticity of demand between it and good Y is -6. Determine how much the consumption of this good will
- The general demand function for good A is Qd = 754 + 2PA - 0.05M + 6 PB + 10 T + 3 PE + 2N where Qd = quantity demanded of good A each month, PA = price of good A, M = average household income, PB = price of related good B, T = a consumer taste index rang
- If the price of a good starts out above the equilibrium price, then: (check all that apply) a. Consumers will lose welfare due to lower consumption b. Consumers will compete to bid the price down c. S
- Assume that the demand curve for an individual is given by: X= 100 - 0.5 Px. a. What would be Consumer Surplus if price is 10? b. What would be change in Consumer Surplus if price increases to 20?
- The linear demand function, the log-log demand function and two alternative forms of the semi-log demand function are simple formulas for demand functions where the quantity of a good demanded is represented as a function of its price and the consumer's i
- Suppose the market demand for a good is described by the equation P = 40 - 0.5 Q. If a change in market supply results in price decreasing from P_0 = $30 to P_1 = $25, then find the resulting change in consumer surplus.
- Suppose that the supply of a good is perfectly elastic at a price of $5. The market demand curve for this good is linear, with zero quantity demanded at a price of $25. Given that the slope of this linear demand curve is -0.25, draw a supply and demand gr
- Suppose consumers A and B have the following demand functions for x. x^A(I, p_x, p_y) = \frac{1 + p_y}{p_x}, x^B(I, p_x, p_y) = \frac{p_y}{1 + p_x} For each consumer, is x a normal good or an inferior good? Explain why.
- The generalized demand and supply functions for good X are Q_d = 10 - 2P_X + 2P_Y + M and Q_s = 10 + 2P_X. A. What is the demand function when P_Y = $2 and M = $500? B. Use the demand function you found in part A and solve for the equilibrium price (P_o)
- a) If the price in a competitive market is $30, and the demand curve is given by the equation P = 90 - 3Q, then the consumer surplus will be: b) If the price in a competitive market is $30, and the s
- Suppose that a consumer consumes two goods x and y. The price of good x falls (and nothing else changes). After the price change, the consumer buys more of both goods.
Explore our homework questions and answers library
Browse
by subject