Suppose an individual demand curve is given by P = 50 - 5Q, where P is the price of pizza and Q is the quantity she consumes. Assuming her income per week is $500 and the current price of pizza is $10 each, by how much will her consumer surplus decline if the price of pizza increased to $15 each?
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- Suppose that Alex's marginal rate of substitution (MRS) between good A and B is always equal to -2. The prices of the goods are $5 and $4 respectively. Alex's income is $20. Thus, his optimal consumption bundle must be (x*1,x*2) = (4,0), i.e., his demand for good A and good B is x*1 = 4 and x*2 = 0, respectively. Is this true or false? If true, show the steps in full to justify and if it is false, show the correct demand and expalin in details.A consumer’s budget set for two goods (X and Y) is 600 ≥ 3X + 6Y. (LO2) a. Illustrate the budget set in a diagram. b. Does the budget set change if the prices of both goods double and the consumer’s income also doubles? Explain. c. Given the equation for the budget set, can you determine the prices of the two goods? The consumer’s income? Explain.a. Determine the demand functions of x and y in the case of a Cobb-Douglas type utility function, in the following cases: α=0.40;β=0.60 Graph the demand functions of the two goods (price as a function of quantity) assuming the individual's income is $500 - Determine what is the quantity demanded of x and y, if the price of good x is USD 1, the price of good y is USD 4, and income is USD 500 - Now, explain what happens to the quantity demanded if the prices of the goods are doubles holding income constant.
- 5 Suppose the quantity of good X demanded by individual 1 is given byX1 = 10−2PX +0.01I1 +0.4PYand the quantity of X demanded by individual 2 isX2 =5−PX +0.02I2 +0.2PY a) What is the market demand function for total X (= X1+X2) as a function of PX, I1,I2, and PY . b) Graph the two individual demand curves (with X on the horizontal axis,PX on the vertical axis) for the case I1 = 1000, I2 = 1000, and PY = 10. c) Using these individual demand curves, construct the market demand curve for total X. What is the algebraic equation for this curve? d) Now suppose I1 increases to 1100 and I2 decreases to 900. How would the market demand curve shift? How would the individual demand curves shift? Graph these new curves. e) Suppose PY rises to 15. Graph the new individual and market demand curves that would result.A consumer’s preferences over two goods x and y are given bythe utility function U(x, y) = x^αy^β with α, β > 0. The prices of the goods are px = 2 and py = 4.The consumer has an income of I > 0.• For what values of α and β are these utility functions strictly monotone?• For what values of α and β will the consumer demand (i.e., Walrasian demand) be more x than y?• For what values of α and β are these goods gross substitutes? For what values of α and β are these goods gross complements? Provide a justification for your answer.5. Consider a consumer whose utility function isu(x,y) = sqrt(xy) (MRS(x,y)=y/x)a. Assume the consumer has income $120 and initially faces the prices px = $1 and py = $1. Howmuch x and y would they buy? Draw the budget constraint and the demands. b. Next, suppose the price of x were to increase to $2. How much would they buy now? Draw thisin the same figure.c. Decompose the total effect of the price change on demand for x into the substitution effect and theincome effect. That is, determine precisely how much of the change is due to each of thecomponent effects. (Hint: See the lecture notes for the two properties that determine the locationof “z”, the reference point for distinguishing the income and substitution effects.)
- A consumer’s preferences over two goods x and y are given bythe utility function U(x, y) = xαyβ with α, β > 0. The prices of the goods are px = 2 and py = 4.The consumer has an income of I > 0.(a) For what values of α and β are these utility functions strictly monotone?(b) For what values of α and β will the consumer demand (i.e., Walrasian demand) be more x than y?(c) For what values of α and β are these goods gross substitutes? For what values of α and β are these goods gross complements? Provide a justification for your answer.Assume that the prices of good X, Y and Z are as follows R5,R1 and R4 respectively, and the Judith has an income of R37 to spend. HOW much of each good will judith consume in order to maximise her utility? What will be her total utility and marginal utility of the last rand spent on each good? Show all the calculationsSuppose Alex’s utility function for appleand orange is U(a, o) = a^2o. The price of an apple is $ 4, and the price of an orange is $ 2. Alexhas $ 120 to spend on these two goods.– at the bundle (a, o) = (4, 2) the marginal rate of substitution MRS(a, o) = ____??– Given prices, income, and utility function, the best affordable bundle for Alex is a∗ = __ ?and o∗ = __?
- Jack derives utility from Hokey course (H) and Chess course (C) as given by the following utility function:U (H, C) = √HCThe average price for the hokey course is 20 dollars and for chess course16 dollars. Moreover, Jack has a budgetof 80 dollars. c) Find the income level which is necessary to make Jack reach the same utility level as before theprice change.d) Compute the quantities demanded with the new prices and the income you found in section c.e) Compute the quantities demanded with the new prices and the original budget of 800 dollars.Columns 1 through 4 of the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are $18, $6, $4, and $24, respectively, and that Ricardo has an income of $105. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? How many dollars will Ricardo choose to save? Check your answers by substituting them into the algebraic statement of the utility‑maximizing rule. In other words, show it works when using this rule.Columns 1 through 4 in the following table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are, respectively, $18, $6, $4, and $24 and that Ricardo has an income of $106. a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule.
