2. For the Income-Consumption Line & Engel Curve: (kindly place Good A on the X-axis & Good B on the Y-axis) If the consumer's tastes are given by the Indifference curves schedule and Pa = P1.00, Pb = P1.00 and original budget = P10.00, what happens if budget decreases to P6.00 and then increases to P14.00, assuming that tastes and prices of the two goods are constant. Create the new budget schedules. Plot the 2 new budget lines as well as the original with the 3 indifference curves together and determine the tangency points or LCPC and create the Income- Consumption Line.
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- 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).7. Suppose U = x₁x2 and the budget constraint is given as x₁ + 1 = B, solve for x and 1-α 8. Suppose U = xx and our budget is given as p₁x₁+P2x2 = m, where m is our income. Solve for solve for x and x₂. 9. Suppose now we want to minimize our expenditure while achieving a certain amount of utility. So say our budget is given as P₁x₁ + P2x2, which we want to minimize, while our utility x and x = u, where u is the level of utility we would like to achieve. Solve for x and x₂.Draw two axes: on the horizontal axis (x-axis), represent the quantity of good x, and on the vertical axis (y-axis), represent the quantity of good y. Plot the initial budget line. The equation for the budget line is m = px * x + py * y. You can rearrange it to solve for y: y = (m - px * x) / py. With given values for m, px, and py, you can plot the line that represents all combinations of goods x and y that the consumer can afford. Plot the indifference curves. These curves represent the combinations of goods x and y that give the consumer the same level of utility. Due to the complexity of the given utility function U(x, y) = xy / (x + y), it may be challenging to plot the exact indifference curves. As an alternative, you can use a simpler utility function for demonstration purposes, such as U(x, y) = x^a * y^b (where a and b are positive constants), which results in easier-to-plot curves. Locate the initial optimal consumption bundle, which is the point where the budget line is…
- 1. Is it impossible for two indifference curves to intersect one another? why? 2. What does it mean that preferences are complete? Now would the real-life implica- tions of this assumption look like?What is the logarithmic transform of the utility function U=xα1xβ2xγ3 given the budget constraint px1x1+px2x2+px3x3=M . Select one: a. ln U=ln xα1+ln xβ2+ln xγ3 b. ln U=ln xγ1+ln xβ2+ln xα3 c. ln U=α ln x1−β ln x2−γ ln x3 d. ln U=α ln x1+β ln x2+γ ln x3Suppose a consumer has utility function U(X, Y) = X2/3Y1/3. Suppose the consumer has M =$90 to spend and the prices of goods X and Y are PX = $15 and PY = $6 . a. Carefully express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the…
- You have $3,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that your utility function is U(TM) T1/3M2/3. a. What combination of T and M will you choose? b. Suppose that the price of day trips rises to $50. How will this change your decision?Draw YOUR indifference curve for the consumption of two goods (you pick the goods – be creative!) Make sure to include labels. Why did you choose these two goods? Why do you view these as being a tradeoff? Carefully explain why the indifference curve has the shape you created. (Hint: Discuss the slope. What it means and how it changes) Determine a budget that will be allocated towards your consumption of these two goods. Given the budget, prices for the goods, and your preferences, how will you find the utility-maximizing combination? Give an intuitive answer as well as a graphical answer (make sure to label the graph accordingly).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.
- A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good she prefers more to less) chooses optimally to consume 12 units of X. If the prices change and now pX = 6 and pY = 4, what is the possible range for her optimal X consumption? (like, x >/ 7 or 10 >/ x >/7…etc. Use indifference curve analysis on a graph to reason about the possible locations of the new optimal bundle.)Why is the consumer’s MRS equal to the price ratio at the optimal consumption point? Givea graphical interpretation of this fact in XY space (hint: what do we know about the indifferencecurves and the budget line?).Alex has a monthly budget of $72 to spend on commuter train trips and organic pasta. Each train trip costs $12; each box of pasta costs $6. Alex's preferences for train travel and pasta are represented by the indifference map on the following page. a. Determine which line (L1, L2, L*, or L**) represents Alex's budget constraint. b. Find their utility-maximizing bundle (E1, E2, e*, or e**). How many train trips will Alex take? Suppose the state government establishes a program to subsidize public transportation for commuters, such that each train trip now costs Alex $6. c. Determine which line (L1, L2, L*, or L**) represents Alex's new budget constraint. d. Find their new utility-maximizing bundle (E1, E2, e*, or e**). Determine how many train trips Alex will now take. e. Find the size and direction (positive or negative) of the substitution effect for train trips. As part of your answer, state the starting quantity and ending quantity of train trips that represent this effect. f. Find…