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- QUESTION 1 For the utility function U = (Qx0.5+Qy0.5)² and the budget 133 = 8Qx + 10Qy find the CHANGE in optimal consumption of Y if the price of X increases by a factor of 1.1. 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).A consumer has a budget of $3000 in a given period, and wishes to buy two goods, X and Y, so as to maximise his utility. The price of good X is $5 and the price of good Y is $2, and his MRS is given by the formula 2Y/X. How many units of good X will he buy in that period?A decrease in the price of good Y will have what effect on the budget line on a normal X-Y graph? Select one: OA. Parallel outward shift of the line OB. Parallel inward shift of the line OC. Decrease the horizontal intercept COD. Increase the vertical intercept
- sketch a person’s indifference map and budget line for two goods, X on the horizontal axis and Y on the vertical axis. Mark the optimum consumption point. Now illustrate the following (you might need to draw a separate diagram for each): (a) A rise in the price of good X (a normal good), but no change in the price of good Y. (b) A shift in the person’s tastes from good Y to good X. (c) A fall in the person’s income and a fall in the price of good Y, with the result that the consumption of Y remains constant (but that of X falls).U=X^0.7*Y^0.8 utility function (EXAMPLE: U=XL In the Utility function given above, U=Utility level, X and Y are two goods such as apples and pears) (e.g. apple and pear),Px and Py represent the price of goods X and Y, respectively. (M) shows income The budget equation is shown as M=PxX+PyYpx=5py=10M=800a) Find the Y quantities that maximize the Utility according to the above. b) Calculate how much a one-unit increase in the constraint will increase the level of utility. c) Calculate the maximum benefit levelNo written by hand solution 1. Thomas consumes only pizzas (Z) and burritos (B). His utility function is given by U(Z, B) = Z · B. The price of a pizza is pZ and the price of a burrito is pB. Thomas has Y dollars. (a) Draw Thomas’s indifference curves and budget line if pZ = 20, pB = 10, Y = 100. (b) Find the optimal amount of pizzas and burritos Thomas will buy if pZ = 20, pB = 10, Y = 200. (c) Derive Thomas’s demand function for pizzas if pB = 5 and Y = 5. (d) Is Thomas better off if i) pizzas and burritos become twice cheaper, or if ii) his income doubles? (e) Suppose Thomas enters a cafeteria and discovers that pZ = 10 and pB = 25 (burritos are really delicious there). Thomas has Y = 200 in his pocket and would like to make an optimal choice. However, he is told that there are only two burritos left. Draw the budget constraint and find the optimal consumption bundle. 2. Thomas consumes only beer (B) and Internet (I). He subscribes to an Internet provider that charges 2…
- Assume that a consumer can buy only two goods, X and Y, and has an income of $13,000. The price of X is $60 and the price of Y is $140. What is the slope of the budget line if X is measured horizontally and Y is measured vertically? Note that you will need to include a negative sign in your answer. If needed, round your answer to the nearest two decimal places.Suppose the price of a donut is $2.50, the price of a cinnamon roll is $3.20, and the budget is $50. Donuts are on the x-axis and cinnamon rolls are on the y-axis. If the price of a donut increases to $3.30, what happens to the Budget Line? The budget line undergoes a parallel shift outward The budget lines undergoes a parallel shift inward The budget lines rotates outward The budget lines rotates inwardA consumer has utility (see image) on ice creams (x) and cakes (y). (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x). (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.
- For the utility function U = (Qx0.5+Qy0.5)² and the budget 122 = 8Qx + 8Qy find the CHANGE in optimal consumption of X if the price of X increases 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).Given the following budget constraint: PXQX + PYQY = M, where PX = $2, PY = $1 and M = $10 (M is income) a. What is the slope of the budget constraint in QX/QY space (where QX is on the horizontalaxis and QY is on the vertical axis)?b. What is the relative price of an additional unit of X?c. What is the relative price of an additional unit of YSuppose you have a $20 gift card and want to buy Blue and Red yarn. The utility function from yards of blue (B) and red (R) yarn can be expressed as follows: U(B,R) = 3B+R Red yarn costs $4 per yard. blue yarn costs $4 per yard. A) Graph the budget constraint and the indifference curves that can be reached. How many yards of each type of yarn will he purchase at these prices with his gift card?
