Problem 3 (10 points; 5 points for each part): Richard has a total utility function of: TU=10q₁ q₁² +2492-92² +9192, where q₁ and q2 are goods. Richard is currently consuming at q₁ = 4 and q₂ = 6, which is also his utility maximizing consumption level. (Richard's optimal point is an interior solution). (a) (b) How much additional utility would Richard receive if he were to increase his consumption of q2 from 6 to 7? (5 points). How much q2 is Richard willing to pay (in terms of q2) in order to consume the 5th unit of q₁? (5 points).

Please get correct

PROBLEM (4) You have the Cobb-Douglas utility function u(x, y) = xy over apples (x) and plums (y) and you have $120 budget to spend and can carry at most 480 ounces in weight in your backpack going back to the dorm. Each apple costs $1 and weighs 8 ounces, and each plum costs $3 and weighs 4 ounces. You can only leave the store with a bundle of fruits you can afford and carry. (a) Drawing the relevant lines, intercepts, marking the points and hence identifying the feasible set of bundles, calculate the optimal bundle. (b) Forget about (a). If you were to choose a backpack before going on this shopping trip, for the weight constraint not to be an issue for you, how many ounces of weight capacity would you need for your backpack? HINT: That is, for this weight capacity of the backpack, you'd be able to carry the best bundle you can afford, i.e, the weight constraint is not binding for your decision. (c) Forget about (b). In (a), just before going out for shopping with your backpack to…

3. Consider the following utility function: U = 5 x1 + 2 x2 Also consider the following bundles: A=(6, 6) B=(8, 4) C=(4,11) D=(7, 9) E=(9, 3) If x1=20, how much of x2 does the consumer has to consume to obtain a utility level of 150?   50   300   170   25

For the utility function U = Qx0.28Q (1-0.28) and the budget 137 = 11Qx+6Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.6. 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).

For the utility function U = Qx0.46Qy(1-0.46) and the budget 100 = 11Qx + 11Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.5. 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).

Find the expenditure function corresponding to utility function u(x₁,x₂) = ln(x₁ +a)+ln(x₂+b). a.e(p₁u) = 2√P₁P₂)eu/2 b.e(p,u)=e¹(√P₁P₂)+ap₁ + bp₂ Ⓒc. e(p₁u) = 2(√P₁P₂)eu/2-ap₁-bp₂ d.elpu)=e"√√P₁P₂

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).

Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) isrepresented by the utility functionz; u(x, y) = xy + x + y Suppose now that Reese’s income is high relative to the prices of peanut butter andchocolate (more concretely, imagine I > px and I > py). What is Reese’s Marshalliandemand for peanut butter, x^∗(Px, Py, I)?

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).