The Calculus of Demand Calculus Appendix Figure It Out: Question 1 of 3 Antonio gets utility from burgers (B) and fries (F). His utility function is U(B, F) = √√√BF = B0.5 F0.5 Antonio's income is $20, and the price of fries is $2. Derive Antonio's demand for burgers. Use symbolic notation and fractions where needed. B =

The utility function for Morris is U = min {AM, T}, where M is pints of milk and T is cans of tuna. Morris has S90 to spend or tuna (prices at $2 per can) and milk (priced at $1 per pint). What is Morris's utility-maximizing consumption bundle?  1)M = 40 and T= 25 2)M= 15 and T= 65 3)M= 10 and T= 40 4)M= 30 and T= 30

Assume that Bob's utility function over beer x and pizza y is U(x,y) = 4x+12y. Which of the following statements is false? a) If the price of pizza is 12 and the price of beer is 3, then we can't determine how much pizza relative to beer Bob purchases. b) If the price of pizza is 16 and the price of beer is 5, then Bob only purchases pizza. c) If the price of pizza is 15 and the price of beer is 5, the own price elasticity of the demand for pizza as well as beer is infinite. d) It the price of pizza is 15 and the price of beer is 4, Bob purchases only beer e) Pizza and beer are perfect substitutes.

Let U(x, y) = 3x + y be the utility function of a consumer, whohas a budget of I. As a function of I, find the consumer’s Walrasian demand when the prices are px = py = 1. The price of good x increases to 2, find the new Walrasian demand for the new prices    px= 2 and py = 1. Decompose this change into an income and a substitution effect.

There are two goods, apples and bananas. The price of apples is PA = $2,and the price of bananas is PB = $3. A consumer has $120 to spend, and his utility function is U(A,B)=2A2B3 a) With apples on the x axis, the slope of the budget line is ________ b) At A=2, B=1, the marginal utility of A is  and the marginal utility of B is ________ c) At the optimal bundle, the consumer buys  apples and  bananas ______

Let U(x, y) = 3x + y be the utility function of a consumer, whohas a budget of I. As a function of I, find the consumer’s Walrasian demand when the prices are px = py = 1. The price of good x increases to 2, find the new Walrasian demand for the new prices px = 2 and py = 1. Decompose this change into an income and a substitution effect.

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Ben gets utility from apples and bananas and his preferences can be represented by the utility function U(A,B)=4A+B. If the price of apples is 3 times the price of bananas, what is Ben's ordinary demand function for apples, A*(p A, P B, I)? OA (P A, PB, 1)=0 A*(p A, P B, 1)=1/P A OA (P A, PB, 1)=21p A OA (P A, PB, 1)=1/(3p A) O A*(p A, P B, 1)=1/(4p A

Based on Nick's willingness to sell, plot his supply curve as a step function on the following graph using the orange points (square symbol). Be sure to plot your first point at (0, 0). Price of Water 10 9 100 8 7 8 10 3 2 1 0 0 2 3 Quantity of Water Suppose the price of a bottle of water is $4. In this case, Nick receives $ 5 If the price rises to $6, Nick now sells Nick's Supply Price = $4 Use the black line (plus symbol) to draw a price line at $4. Next use the grey point (star symbol) to indicate how many bottles of water Nick will produce and sell at that price. Finally, use the purple point (diamond symbol) to shade the area that represents Nick's producer surplus. bottles of water. This Quantity Sold Producer Surplus in producer surplus from his water sales. his producer surplus to $

1.3. Consider the following utility function for a consumer who consumes two goods, x1 and X2, and answer the questions below: u(x1, x2) = In(x1)+ x2 (a) Calculate the marginal rate of substitution (MRS) for this utility function. (b) Does u(x) exhibit strictly monotonic preferences? Explain. (c) Is u(x) a homothetic function or not? Explain. (d) Is u(x) quasi-concave/quasi-convex/neither where x1 0? Provide support for your an- swer.