The utility function of a consumer is given as follows. U(x, y) = x?y3. MU, = 2xy3 and MU, 3x?y2. %3D %3D a. Derive the demand functions for good x and good y. b. Draw a demand curve. Draw an Engel curve. Is good x a normal good? C.

Imagine Billy eats brownies (B) and cookies (C) and considers them to be perfect substitutes. Brownies yield him four times more utility than cookies. Which of the following equations could describe his utility function? U= 0.25B + C O U=B+ 0.25C U = B'C OU = BC4 %3D

16.Suppose the market for a good is composed of 1,000 identical consumers. The market's demand curve is given by QM = 150,000 – 25P. What is the equation for an individual consumer's demand curve? A) Q = 150,000,000 – 25,000P B) Q = 6,000,000 – 40P C) Q = 6- 4P D) Q = 150 –0.025 17.There are 100 consumers in the market for good X. each with a demand curve given

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A consumer’s preferences over two goods x and y are given bythe utility function U(x, y) = xαyβ with α, β > 0. The prices of the goods are px = 2 and py = 4.The consumer has an income of I > 0.(a) For what values of α and β are these utility functions strictly monotone?(b) For what values of α and β will the consumer demand (i.e., Walrasian demand) be more x than y?(c) For what values of α and β are these goods gross substitutes? For what values of α and β are these goods gross complements? Provide a justification for your answer.

Question 3: Robert's utility is given by U(x,x)=ln x + ln y, and therefore MUX-1/x and MUX-1/y. Let the prices and income be Px. Py and m. a. Find Robert's demand for x and y b. How is Robert's demand for x affected by an increase in Py? Explain

Assume one person has the following utility function : = x f yz and the total income y 2 xpx+ yPy + zpz u( x, y, z, What are the values of income (y) and prices (px.Py,Pz) will be when a person's demand strictly positive quantity of good x?

A consumer's utility function is given by (x₁+x₂); with MU and MU wherex, and x, denote the quantities of good 1 and good 2 consumed. 1 2 Calculate the utility maximizing quantity of good 1 if income is 397, price for good 1 is 6 and price for good 2 is 8. Please round your answer to the closest integer.

Bob has utility function U(x,y)=x2+y over goods x and y a) Do we have a name for this type of utility function? Are Bob's preferences well-behaved? b) Let Bob have budget I=$60, and let prices be Px=$30, Py=$10. Find Bob's optimal basket of goods x and y. Is this an interior or corner solution? c) What will happen if the price of good y doubles? [Think about: can we use this utility function to describe preferences over pet snakes and pet mice?]

12) A consumer’s preferences are given by U(X,Y) = X0.6Y0.4. The price of X is 4, and the price of Y is 5. The consumer has an income of $2000.a) What is the utility maximizing choice of X and Y?b) How would the utility maximizing choice change if price of X falls to 3 because of a pricesubsidy?c) Given the answers to the previous parts plot a linear demand function for X.d) Show that the consumer would prefer the cash equivalent of the price subsidy in part b.