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Optimisation in levels is the optimal amounts to get maximum profit or maximum consumption of a good and service.
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- Ding Ding is a cat philosopher. He spends his time on two activities. Sleep and thinking. Both activities produce pleasure to Ding Ding. How effective Ding Ding is in each activity varies day by day. But on a given day, if he spend “s” effective hours in sleeping and “t” effective hours in thinking, his utility is u(s,t)=s^2+t. you can assume that time is continuous in answering the following question. (A) Let us first ignore that there are only 24 hours each day. Label “s” on the x-axis and “t” on the y-axis in a diagram. Draw two indifference curves u(s,t)=s^2+t=24^2=576, and u(s,t)= s^2+t=12^2=144. On each indifference curve, you have to mark at least the coordinates of four points to illustrate the shape of it. (B) Describe in words how these two indifference curves in (a) relate to each other.1. Jan has the following utility function for broccoli: U(B) = 54B - 0.5B³ a) What is Jan's marginal utility function?For the following utility function find the MRS at (x, y) = (2, 3) a) U(x, y) =2x +y b) U(x, y) =x^3 y^2 c) U(x, y) =min(x, 2y) Solve subparts (c )correctly
- 1 explain the role of ceteris paribus in economic analysisAs a consumer you have RM34 per month to spend for snack i.e. either pizzas which costs RM6 each or chicken burger which cost RM4 each. Suppose further that your preference is given by the following Total Utility Table Quantity 1 2 3 4 5 6 7 Pizza 60 108 138 156 162 166 166 Chicken Burger 44 76 100 120 136 148 152 First, graph the budget constraint with Pizzas on the horizontal axis and Chicken burger on the vertical axis. What are the intercepts at horizontal axis and vertical axis. Using the table, please show the Marginal Utility of Pizzas and Chicken Burger for every quantity demand. Using the utility maximizing rule to identify the consumer equilibrium, that is, combination of pizzas and chicken burger that will maximize your Total Utility. Confirm that the consumer equilibrium generates the highest combined total utility of any affordable combination of goods.Matthew Hamming is stranded on an island. He has decided that he will spend exactly 10 hours a day gathering food. He can either spend this time gathering coconuts or catching fish. He can catch 2 fish per hour and he can gather 3 coconuts per hour. Matthew's utility function is U(FC) = 3F0.60.3 a. How many fish should Matthew catch and how many coconuts should he gather so that his consumption maximizes his utility? Illustrate the equilibrium with a graph b. One day a native inhabitant of another island arrives on the island. The visitor offers Matthew trade of 3 fish for 1 coconut. The trade fee costs 1 fish (that must be paid prior to the exchange). Will Matthew decide to trade? What will Matthew produce and consume? Justify your answer and provide a graph.
- 4.An individual consumes products X and Y and spends $30 per time period. The prices of the two goods are $3 per unit for X and $3 per unit for Y. The consumer in this case has a utility function expressed as: U(X.Y) = 0.5XY How much X should this individual consume, given that he is maximizing the utility? ( A) 4.17 ( B) 5 (C)6 D) 6.25solutions. Question 1 Calculating MRS for CD Utility Functions (a) If a consumer has a CD utility function 0.4 0.6 U(91,92) = 994926, calculate MRS1,2. (b) If a consumer has a CD utility function Ima kdown1 calculate MRS1,2. (c) If a consumer has an utility function noltan asd Tor sympy ,1-α U(91,92) = 91 92 llib et (.) orde (hing aid tol bholup U(91,92) = a ln(91) + (1 - a) ln(92), diw sonuanos of calculate MRS1,2. Is it the same as the result in the previous part? (Note: Recall that we discussed the concept of ordinal utility in class, which means only the order of utility matters, not its magnitude. In function is a monotone transformation on the CD utility function. Notice that In (qq) = a ln(9₁) + (1 - a) ln(92). This example verifies that a monotone transformation does not change *(S) sidshav the consumer's indifference curves.) wobei/ (d)The table below shows the marginal benefit that Dan derives by consuming different quantities of tacos and soda .The price of a taco is $3 and the price of soda is $1. Quantity sodas Tacos Marginal benefits ($) Marginal benefits($) 1 10 18 2 8 12 3 6 6 4 4 3 5 2 1 6 1 0.6 Refer to the table above.If Dan consumes 3 tacos and 0 sodas -not necessary his optical choice- how much consumer surplus is he enjoying? a) $ 24 b) $ 27 c) $ 9 d) $6
- c and d pleaseSuppose a student has monthly income of Rs 20,000. He consumes only two commoditiesSandwich and Shawarma. The cost of Sandwich is Rs 100 each, and the cost of Shawarma isRs 200 each.a) Draw the student’s budget constraint. What is the slope of his budget constraint?b) Suppose student gets a raise, so his income increases from Rs 20,000 to Rs 24,000. Showwhat happens to consumer optimal consumption choice if both Sandwich and Shawarmaare normal goods. Now show what happens if Sandwich is an inferior good.c) Suppose consumer income decreases to Rs. 16,000. Show what happens if both Shawarmaand Sandwich are normal goods. Now show what happens if Sandwich is an inferior good.If the utility function (U) between food (F) and clothing (C) can be represented as U = F*C, then which combination of food and clothing will a rational consumer choose? a. (F, C) = (9, 25) O b. (F, C) = (25, 4) O c. (F, C) = (4, 16) d. (F, C) = (4, 25)