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- A consumer has the following utility function: U(X1,X2) = X1X2 + X1 + 2X2Where X1 is her consumption of candies with a price of $2 and X2 is her consumption of notebooks with a price of $5. Her income is $51. Determine the number of candies andnotebooks that will maximize the consumer’s utility.A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizzaCharlie's utility function is (1-a) U(xa, XB) = Ax“xr-) where A > 0 and a > 0
- Questions 1. Will's utility from vacations (91) and meals (92) is given by the function U(V, M) = 91 x 92. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, while the price of vacations remained the same. Both years, Will had an income of $1500. (a) What is the compensating variation for the price change in meals? (b) What is the equivalent variation for the price change in meals?Suppose a consumer has the following utility function: U(x1,x2) = alnx1 + (1-a)lnx2. The price of good 1 is $10 and the price of good 2 is $20 and the consumer’s income is $500. Find the quantities of x1 and x2 that will maximize utility if a=1/2.A consumer has utility function U(x1, X2, X3, X4, X5, X6, X7) = min{/x1x2, /X3X4, VX5X6X7} Find the demand function. 3)
- The utility function of a consumer is u = √x + 2y. (a) Calculate how much MRS of that consumer when x = 4. (b) If the consumer currently consumes 4 units of goods x and the price ratio of Px / Py = 1/4, then the consumer should increase or decrease the consumption of goods x?What is the logarithmic transform of the utility function U=xα1xβ2xγ3U=x1αx2βx3γ given the budget constraint px1x1+px2x2+px3x3=Mpx1x1+px2x2+px3x3=M. Select one: a. ln U=ln xα1+ln xβ2+ln xγ3ln U=ln x1α+ln x2β+ln x3γ b. ln U=α ln x1−β ln x2−γ ln x3ln U=α ln x1−β ln x2−γ ln x3 c. ln U=α ln x1+β ln x2+γ ln x3ln U=α ln x1+β ln x2+γ ln x3 d. ln U=ln xγ1+ln xβ2+ln xα3Suppose a consumer has a utility function given by U(X,Y) = MIN(X, 2Y). The consumer has $90 to spend (M = $90). The Price of good Y is Py = $1. a) Draw the consumer's Price Consumption Curve for the following prices for good X: Px = $1, Px = $2, Px = $2.5. For each set of prices, make sure to accurately draw each budget constraint, and also identify the consumer's optimal bundle on each budget constraint. Make sure your graph is neat, accurate, scaled properly, and fully labeled to receive full credit.
- Consumer utility function is, U(XY) = X 75 Y 0.5. The price of X good 2 AZN and Y good 4 AZN. If consumer utility is maximum and consumer buy 12 unit X goods, find how much consumer can buy Y goods.Anna has an income of 1000 euros and utility function U(x,y)=x²y³. The prices of the two goods are P₁=5 and Py-20. a) Define the budget constraint and represent it graphically. (Assume that a person's utility function is given by the following function: TU = 2x/2y/2 Assume also that the price of X is £2, and the price of Y is £6 and that the budget is £240. What is the optimal amount of goods X and Y that should be purchased with this budget?
