Suppose you have $120 to spend on food and clothing. The price of food is $4 and the price of...
Question:
Suppose you have $120 to spend on food and clothing. The price of food is $4 and the price of clothing is $8.
a. Graph your budget constraint; calculate the slope of it.
b. Briefly explain why your optimal choice is the point at which your budget constraint is tangent to an indifference curve.
Budget Constraint:
The combinations of goods and services that a consumer can purchase with the income at his or her disposal based on the current prices of those goods and services can be expressed in form of a budget constraint. The budget constraint shows that because the total cost of the goods and services in the consumer's basket cannot exceed the income, to consume one more unit of one good or service, some units of another good or a service has to be given up.
Answer and Explanation: 1
a. Graph your budget constraint; calculate the slope of it
Let food be F and clothing C such that the budget constraint is expressed as follows:
{eq}$4F + $8C = $120 {/eq}
{eq}F = $30 - 2C {/eq}. The graph of this budget constraint is given as follows:
![]() |
The slope of the equation can be computed as {eq}\frac{\Delta F}{\Delta C} = -2 {/eq}
b. Briefly explain why your optimal choice is the point at which your budget constraint is tangent to an indifference curve.
When maximizing utility, the consumer is constrained by the budget constraint. For any bundle that the consumer chooses to derive utility from, their total expenditure cannot exceed the budget. Since the consumer is rational, they will prefer to consume at a higher indifference curve. Utility is only maximized when the budget constraint curve and indifference curve and as the consumer chooses a higher indifference curve, the highest indifference curve is the one that is tangent to the indifference curve. It is the point when the slope of the budget constraint is equal to the slope of the indifference curve. It is the point where marginal rate of substitution of one good for another equals the ratio of their prices. That is, {eq}MRS_{xy} = \frac{P_X}{P_y} {/eq}
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:

from
Chapter 3 / Lesson 2Learn about utility maximization. Discover various types of utility, examine utility maximizing rules, and study examples of maximizing utilities in economics.
Related to this Question
- Assume that you have $100 to spend on food and clothing. The price of food is $5 and the price of clothing is $10.a. Graph your budget constraint.b. Suppose that the government subsidizes clothing suc
- Assume that the budget constraint shown is for $600 of income with a price of food equal to $2 and a price of clothes equal to $4. With an indifference curve and budget constraint as shown, will a TANF grant of $200 have the same effect on food consumptio
- Assume that you have a budget of $25 to spend on milk and cereal only. The price of milk is Pm = $4.00 and the price of cereal is Pc = $5.00. 1. Graph the budget constraint. Be sure to put the quantit
- Jane has $1000 a week to spend on clothing (C) and food (F). The price of clothing is $20 and the price of food is $10. 1.Write the equation for Jane's budget constraint. Y=M/Py-(Px/Py) X Y=Quanti
- Draw the budget constraint for a person with income of $1,000 if the price of Pepsi is $5 and the price of pizza is $10. What is the slope of this budget constraint?
- Assume that you have a budget of $30 to spend on milk and cereal only. The price of milk is PM = $5 and the price of cereal is PC = $3.50. a) Graph the budget constraint. Be sure to put the quantity
- All there is are movies (m) and food (f). The price of movies is $10 while the price of food is $5. I have $145 to spend on these two goods. My preferences are described by the following utility function: u(m, f) = m + f + mf. Graph the budget constraint
- Put meat on a horizontal and potatoes on a vertical axis. Suppose your income is $1000, prices of meat and potatoes are $10 and $20, respectively. Find the budget constraint equation, and draw the budget line. Explain what the two intercepts mean.
- You spend your entire budget on coffee and doughnuts. Each doughnut costs $2 and a cup of coffee costs $1. a) What is the slope of your budget constraint? Interpret it. Suppose, one of the following t
- a) Draw a budget line for someone who has an income of 50 and buys two goods, food and clothing. put food on the x-axis. The price of food is 7.5 per unit and the price of clothing is 5 per unit. b) T
- Suppose you have drawn a consumer's budget line for food and clothing with food on the horizontal axis and clothing on the vertical axis. If the price of food increases: A. the budget line becomes flatter. B. the budget line becomes steeper. C. the budget
- Graphing the BC. Suppose that an individual has a weekly income of $180 to spend on goods X and Y, which have prices of $2 and $6, respectively. Graph the budget constraint. Suppose that the price of
- Assume that food is measured on the horizontal axis and clothing on the vertical axis. If the price of food falls relative to that of clothing, the budget line will: a. Become flatter, b. Shift outward, c. Become steeper or flatter depending on the rel
- a) Draw the budget constraint for a person with an income of $1,000 if the price of Pepsi is $5 and the price of pizza is $10. b) Choose any combination of pizzas and from the table and write a proper budget equation with Pizza denoted as good x and Peps
- Zenna buys only apples and bananas. The price of apples is $2 a pound and the price of bananas is $1 a bunch. She has $20 to spend on apples and bananas. a) Write the equation of her budget line or budget constraint. b) If she spends all of her money on a
- You spend your entire budget on coffee and doughnuts. Each doughnut costs $2 and a cup of coffee costs $1. a. What is the slope of your budget constraint? Interpret it. Suppose, one of the following two things happen to you tomorrow. Situation 1: Someone
- 11. A consumer has $400 in income, the price of food is $1 and the price of Y is $1. Also, the consumer has $100 in SNAP benefits that can only be used for food. BCno S is her budget constraint with n
- Your income is $40. The price of each unit of food is $2, and the price of each unit of clothing is $10. Draw a graph of your budget line. Now, your income rises to $50 and the prices of food and clot
- Thembi has a budget of $1400 and the price of food is $200 and the price of clothing is $100. She maximises her utility by buying 4 units of food and 6 units of clothes. Draw a budget line with food on the horizontal axis.
- Your budget is $50. The price of amusement goods is $10. If the price of clothes falls to $4, which of the following statements is true? a. The marginal-utility-to-price ratio for clothes will decrease. b. The marginal-utility-to-price ratio for clothes w
- The equation for a budget line for goods X and Y, with P_x being the price of X, P_y being the price of Y, and B being the budget, can be written as: a. P_x X + P_yY = B. b. P_x X + P_y Y = 1/B. c. P_x X = B + P_y Y. d. {P_x X} / {P_y Y} = 1 - B.
- Suppose a consumer has an income equal to I which he/she spends on either food or clothing. The price of food is given by Pf and the price of clothing is given by Pc. If the consumer spends all of his/her income on clothing, the expression for the number
- Suppose a consumer has an income equal to I which he/she spends on either food or clothing. The price of food is given by P_f and the price of clothing is given by P_c. If the consumer spends all of his/her income on clothing, the expression for the numbe
- Suppose a typical household spends its income on food (F) and clothing (C). Initially, the price of food in $10 and the price of clothing is $20, and the typical household consumes 10 units of food an
- If the consumer's budget constraint is given by 10F + 5S = 100, where F is food and S is shelter, what is the opportunity cost of food in terms of shelter?
- If the consumer's budget constraint is given by 10F + 5S = 100 where F is the quantity of food and S is the quantity of shelter, how much food can he buy with his income remaining if he purchases 2 units of shelter? A. 10 B. 5 C. 20 D. 9 E. None of the ab
- Assume that a consumer has a budget of $45 to allocate over two products, milk (M) and bread (B). The price of milk is PM = $4:50 and the price of bread is PB = $5:50. 1(a): Draw a graph of the budg
- Suppose a consumer has M = $120 to spend. The price of Good X is PX = $2, and the price of Good Y is PY = $3. a) Draw the consumer's budget constraint. Be sure to label your graph accurately, and identify the vertical and horizontal intercepts. (Please pu
- If a consumer's budget constraint is given by 10F + 5S = 100, where F is food and S is shelter, what is the opportunity cost of food in terms of shelter? A. 5 B. 2 C. 15 D. 10
- Assume a specific-factors economy produces two goods, cloth and food, and that when representing the output of this economy graphically, cloth is on the x-axis and food is on the y-axis. When the price of cloth increases by 5% and the price of food increa
- Suppose you have a budget of $1,300 to spend of beer and pizza this year. Your utility function is U = 200B + 150P - 0.5B^2 - 0.25P^2. The price of a beer is $5 and the price of a pizza is $10. a. Using calculus, set up a constrained optimization problem
- Below is the equation the budget constraint for Joe for his coffee (C) and doughnuts (D) consumption. His income is 10, the price of doughnuts is $2 and the price of coffee is $1. Income= 1C + 2D Doug
- An individual has a budget constraint of $28. The price of healthcare is $2 and the price of all other goods is $4. a) Graph their budget constraint. b) Label the axes. In other words, indicate whethe
- Suppose there are two goods (X and Y). On a traditional graph of a budget line a tripling of all prices and incomes will: a. alter the slope of the budget line only b. alter the slope of the budget li
- Suppose Carlos has a weekly budget of $48 to spend on yogurt and juice. Juice is priced at $4 per gallon, and yogurt is priced at $6 per bowl. (a.) Graph Carlos' budget constraint. Indicate the area o
- Joe's income is $500, the price of food (F) is $2 per unit, and the price of shelter (S) is $100. Which of the following represents his budget constraint? a. 500 = 100F + 25 b. 500 = 2F + 1005 c. 5 = 500 - 2F d. All of the above
- Give a graphical representation of the effect on the budget constraint if the price of one good decreases.
- The slope of the budget constraint is determined by the: a. relative price of the goods measured on the axis, b. relative price of the goods measured on the axis and the consumer's income, c. preferences of the consumer, d. Both b) and c) are correct.
- In a simple economy, people consume only two goods, food and clothing. The market basket of goods used to compute the CPI has fifty units of food and ten units of clothing. Food Clothing 2002 Price $
- Samira has a monthly income of $200 that she allocates among two goods: meat and potatoes. a. Suppose meat costs $4 per pound and potatoes $2 per pound. Write the equation for her budget line and draw it. b. Suppose also that her utility function is given
- Carolyn is given a bundle of housing and food that is on her budget constraint. What has to be true about the price of housing and the price of food relative to the MRSFH in order for it to be the ca
- An individual consumes two goods, clothing and food. Given the information below, illustrate the income-consumption curve. |Clothing Price |Food Price| Clothing |Food |Income |$3.00 |$12.00 |200 |5
- 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
- In a simple economy, people consume only two goods: food and clothing. The market basket of goods used to compute the CPI consists of 50 units of food and 10 units of clothing. a. What are the percentage increases in the price of food and in the price of
- Suppose your utility function for food (F) and clothing (C) is U(F,C) = F + 4C. If you reduce your clothing consumption by 2 units, how much do you have to increase your food consumption in order to maintain the same utility level? Explain the answer.
- This graph shows three different budget constraints: __A, B,__ and __C__. If Bart has budget constraint A in the graph shown, what would cause his budget constraint to shift to __B__? a. Bart's income has decreased, b. The price of soda has increased,
- Assume that the price of Good X is $5, the price of Good Y is $4, and the consumer's budget is $100 per month. a. Carefully construct and fully label the consumer's budget line. What is its slope? b
- Jim buys only bananas and CDs. Suppose that Jim's income is $40, bananas cost $0.80 per pound, and CDs cost $8 each. (a) Write the equation for Jim's budget constraint and graph it. (b) Suppose that
- Jim buys only bananas and CDs. Suppose that Jim's income is $40, bananas cost $0.80 per pound, and CDs cost $8 each. Write the equation for Jim's budget constraint and graph it. Suppose that Jim's opt
- The equation for a budget line for goods X and Y, with Px being the price of X, Py being the price of Y, and B being the budget, can be written as: a). P x X + P y Y = B . b). P x X + P y Y = 1 B . c). P x X = B + P y Y . d). P x X P y Y = 1 B .
- Shifts in a budget constraint Paolo brings $30 to a baseball game to spend on sodas and pizza. The following diagram shows his budget constraint: According to the budget constraint the price of soda
- Leyla consumes goods X and Y. The price of good X is P_X and the price of good Y is P_Y. Leyla's income is I. If both prices and Leyla's income decrease by 50%, then the A. slope of the budget constraint will decrease. B. slope of the budget constraint wi
- Assume the price of good X is P X , price of good Y is P Y , and B is the budget. The formula for the budget line for these two goods is a. P Y Q Y P X Q X . b. P X B + P Y B = B . c. P X X + P Y Y = B . d. ( 1 P Y B ) P X .
- Suppose the utility function for an individual is given by u(x, y) = x + y, where x and y are two goods. The budget constraint of an individual is 2x + 5y = 10, where I = 10 is the income of an individual, P_x = 2 - the price of good x, and P_y = 5 - the
- i. A consumer has income of $3,000. Wine costs $3 per glass, and cheese costs $6 per pound. Draw the consumer's budget constraint with wine on the vertical axis. What is the slope of this budget constraint? ii. Show a consumer's budget constraint and ind
- A consumer has an income of $12,120. She consumes only two goods, tacos, and beer. Tacos cost $2.66 each and a bottle of beer costs $3.53. If tacos are on the vertical axis, what is the slope of the budget constraint?
- A consumer has income of $3,000. Wine costs $3 per glass, and cheese costs $6 per pound. Draw the consumer's budget constraint with wine on the vertical axis. What is the slope of this budget constraint?
- A consumer has an income of $3,000. Wine costs $3 per glass, and cheese costs $6 per pound. Draw the consumer's budget constraint with wine on the vertical axis. What is the slope of this budget constraint?
- Consider shopping at a specific grocery store. For each relation, determine the input quantity, the output quantity, and explain why the relation is or is not a function. a.) The cost of a pound of
- You have $10 to spend on goods A and B. The budget constraint is 2 A B 10, assuming non negative values for A and B. a Draw this budget constraint in A,B space. b Mark the affordable region and the un
- Suppose the relative price of clothing has risen over time while the relative price of beef and chicken has fallen over time. Who is the most likely person to be experiencing a rate of inflation that
- Sue consumes only two goods, food and clothing. The marginal utility of the last dollar she spends on food is 12, and the marginal utility of the last dollar she spends on clothing is 9. The price of food is $1.20/unit, and the price of clothing is $0.90/
- A consumer has an income of $39,853. She consumes only two goods, tacos, and beer. Tacos cost $3.03 each and a bottle of beer costs $3. If tacos are on the vertical axis, what is the slope of the budget constraint? (Do not forget to include the sign and r
- Suppose a consumer has $200 in income and purchases 2 items: shirts and pants. Suppose the price of a shirt is $10 per shirt and the price of a pair of pants is $20 per pair of pants. Suppose you hav
- Examine the budget constraint for a consumer who has an income of $4. What is the price of paper? a. $2 each, b. $0.50 each, c. $4 each, d. $1.50 each.
- a) Calculate the MRSx,y b) Write the budget constraint c) What is the consumption bundle to maximize the utility level? What is the maximum utility level?
- Suppose your utility function for food (F) and clothing (C) is u(F, C) = 2F + 4C. If you reduce your food consumption by 2 units, how much do you have to increase your clothing consumption in order to maintain the same utility level? a. 1 unit b. 2 units
- Suppose you are given the following equation for a budget constraint: Good Y = -2*Good X + 500 a) If the price per unit of Good Y is $2, what must be the price of Good X? b) What is the maximum amount of Good X this consumer would be able to purchase?
- Leyla consumes goods X and Y. The price of good X is Px and the price of good Y is Py, Leyla s income is I. If both prices and Leyla s income decrease by 50%, then the A) slope of the budget constraint will decrease. B) slope of the budget constraint will
- Suppose Vivian has a utility function of U = X^{0.4}Y^{0.6}, where X and Y are two goods. The prices for X and Y are $4 and $6, respectively. She has $100 in her pocket. Write down Vivian's budget constraint to buy both goods.
- Joe s budget constraint equals 600 = 2F + 100S, where $600 is Joe s income, $2 is the price of food (F, y-axis) and $100 is the price of shelter (S, x-axis). How much food can Joe buy if he buys one unit of shelter? A) 2 units B) 200 units C) 250 units D)
- Consider Scott who buys two goods - shoes and t-shirts. The price of shoes is $30 per pair and the price of t-shirts is $25 each. Scott has a budget of $300. A) Draw Scott's budget constraint, labeling all the relevant points. B) What is the opportunity c
- a) If the person wants to spend an equal amount of money on both pizza and Pepsi what combination of quantity of both goods needs to be purchased to satisfy the budget constraint? Write the budget equation in this case? b) What happens to the budget equ
- The equation for a budget line for goods X and Y, with Px being the price of X, Py being the price of Y, and B being the budget, can be written as:
- Assume that you can spend a budget of $26.00 on two products, Apples and Bananas. The price of apples (PA) is $3.50 per quantity and the price of bananas (PB) is $3.00 per quantity. The marginal utili
- Suppose Jill has $100 to spend on two goods, shoes and shirts, the price of shoes is $20 per pair and the price of a shirt is $20 each. After spending $70, Jill predicts that the marginal utility to be gained from her next pair of shoes purchased will be
- Assume a specific factors economy produces two goods: cloth and food. When representing the output of this economy graphically, cloth is on the x-axis and food is on the y-axis. When the price of cloth increases by 8% and the price of food does not change
- Connie has a monthly income of $200, which she allocates between two goods: meat and potatoes. a) Suppose meat costs $4 per pound and potatoes cost $2 per pound. Draw her budget constraint. b) Suppose
- An individual has the utility function a) Find his consumption on x_1 and x_2 when his budget constraint is 3x_1+4x_2=100. b) Year later his budget constraint is 3x_1+2x_2=100, find his consumption
- Suppose your friend in the class has decided to purchase a pair of shoes that cost $150 or a dress shirt that costs $100. If she ends up purchasing the dress shirt, then it is possible to conclude that the marginal utility of dress shirt is higher than th
- Create a supply graph that shows the increase of cost to make shoes.
- Jake brings $40 to a football game to spend on sodas and pizza. The following diagram shows his budget constraint: According to the diagram, sodas cost _ each, and pizza costs _ per slice. Adjust t
- a. Diagram 1 shows alternative indifference curves (IC_1 and IC_2) and budget constraint lines (BC_1, BC_2, BC_3) for Jennifer who enjoys consuming tacos with soda. Based on the Budget Constraint BC_1, if the consumer's income is $28, what is the price of
- Suppose a consumer has a daily income of $48 and purchases just two goods, A and B. The price of A is $8 and the price of B is $6. a. Draw the budget line for the consumer in a graph. Indicate the area of the graph that is attainable given the income and
- Fill in the blanks in the table below. Assume the price of a hamburger is $2 and the price of a movie is $5 and the consumer's income is $29. If the consumer is in equilibrium, what is the marginal utility per last dollar spent on movies and hamburgers? A
- Assume that all there is are movies (m) and food (f). The price of movies is $10, while the price of food is $5. Suppose you have $145 to spend on these two goods, and that your preference is described by the following utility function: u (m, f) = m + f +
- Given the set of indifference curves (solid lines) and budget lines (dashed lines) below: a. What would explain the shift from budget line 1 to budget line 2? b. How would the consumption of sweater a
- Assume that you have a budget of $30 to spend on milk and cereal only. The price of milk is $5.00 and the price of cereal is $3.50. a. What is the most you can purchase of cereal? b. If you purchase 3 units of milk, how many units of cereal can you purcha
- Consider the budget constraint below. Dennis spends all his money on sweaters and sweatshirts. If the price of sweaters is $15, what is the price of sweatshirts? a. $5 b. $7 c. $15 d. $21 e. N
- Budget constraints impose scarcity, and are based upon a) the limitation of the budget. b) how much utility one more unit of a good will provide. c) the prices of the items purchased.
- Budget constraints impose scarcity and are based upon: a) the limitation of the budget. b) how much utility is one more unit of a goodwill provide. c) the prices of the items purchased.
- Sam brings $60 to a baseball game to spend on hot dogs and beer. The following diagram shows his budget constraint. A. According to the diagram, what are the prices of hot dogs and glasses of beer? B. Show how Sam's budget constraint would change if the p
- Consider two goods: apples and oranges. Draw an indifference curve diagram that shows apples on the horizontal axis and oranges on the vertical axis, an individual's budget constraint, and the bundle
- Suppose an individual's marginal rate of substitution is three slices of pizza for one beer at the present bundle of beer and pizza she is consuming. If the price of beer is $1.00 and the price of a s
- Budget constraints impose scarcity, and are based upon a. How much utility one more unit of a good will provide b. The prices of the items purchased c. The limitation of the budget