An individual consumes two goods. Let prices and income in periods 0 and 1 be given p° = (pi, p2), yº and ' = (pi, p3), y', respectively. Assume that both prices are 20% lower in period 1 compared to period 0, but ncome did not change. Let the individual's indirect utility function be given by: v(p, y) = y/ /PiP2. Calculate he individual’s equivalent variation.
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Calculate the individual’s equivalent variation.
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- Kamau's utility function for watching football (F) and drinking a soda (S) is given by the function (F,S)=F°S . Last month, the price of a football ticket was Ksh.100 and the price of Soda was Ksh.25. This month the price of soda has risen to Ksh.37.5, the price of a football ticet has remained the same. For both months, Kamau's income has remained to be Ksh750. Calculate Kamau's CS, CV and EV.QUESTION 1 For the utility function U = Qx0.50Qy(1-0.50) and the budget 122 = 8Qx + 14Qy find the CHANGE in optimal consumption of Y if the price of Xincreases by a factor of 1.7. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1).Please draw the income-consumption (or income-offer) curve for each of the following utility functions, indicating the slope of each: (a) U = (A)(x^a)(y^b) (b) U = min(ax, by) (c) U = ax + by
- Eren’s two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V^2MLast year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV).Adrienne consumes three goods, x, y, and z. Her consumption preference is given by the utility function: u(x, y, z) = x*y} z#, (Pz-Py, Pz) where x, y, and z are the quantities she consumes (respectively). Let p = be the prices of the goods. Answer the following questions, and justify your answers carefully and mathematically. (a) Last year p = sumption bundle last year. (1, 10, 10) and Adrienne's income was 35. Find her optimal con- (b) This year, the prices of x and z have both risen 3.5% while the price of y has risen 7%, and Adrienne got an income raise of 3%. Find the (approximate) percentage changes of her consumption in the three goods due to these changes in prices and income. Does her raise adequately compensate her for the changed prices? What additional percentage change of her income would be needed if we were to restore Adrienne to last year's exact utility level?Q.7 A consumer's utility function is given by the expression: & = (0.6.x"s + 9.47"s}. Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X. and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.
- The relationship between a consumer’s income and the quantity of X, he consumes is given by the equation M=1000Q2Suppose an individual has a single period utility function represented by: U = Z²H² Suppose further that the individual is deciding how to spend an hour of their time. Below, you are given information about the meal options and how each meal contributes to the "Home" ("Z") portion of utility and the "Health" ("H") portion. Meal Health (H) contribution to Utility Puzzle Jogging Watching netflix +10 Home Good (Z) contribution to Utility Jogging Watching netflix Doing a puzzle If the individual is in a one-period model, meaning they only care about maximizing utility today, what will they choose? +1 +3 +3 +5 +3Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate for the equivalent variation (EV) for the price change.
- Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should begiven to Eren to offset his change un utility due to the price increase of an expensivemeal. Calculate the compensative variation (CV).Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).Question 2 David spends his budget on chocolate and chip. His utility function is given by ?(?1,?2)= 2?1?2, where ?1 is the number of chocolates he consumers per week, and ?2 is the number of chips he buys per week. A chocolate costs 10 SEK, and a chip costs 20 SEK. David’s weekly budge for consuming on these two goods is 120 SEK. (1) What is David’s budge line? Draw the budget line on a graph with chocolate amounts on the horizontal axis and chip amounts on the vertical axis. Write explicitly at which points budget line crosses the axis. (2) What is David’s marginal utilities for the two goods, respectively? What is his marginal rate of substitution between the two goods? (3) What is David’s optimal choice? Calculate the numerical answer for the optimal bundle. Also draw an indifference curve for David on the same graph as question(1) and show the optimal bundle.