The marginal rate of substitution of Good X for Good Y is MRSXY(x,y)= 9y/x. The price of Good X is PX, the price of Y is PY, and Jane’s income is I. Notice that diminishing MRS is satisfied and preference is smooth. What is the function of the consumer’s demand curve of Good X if income I=100 and price of Good Y is PY=0.2?

Consider a market with two goods, x and z. The consumer’s utility function is U = x^0.2z^0.8 A. Derive the demand function for x and z. B. Let ? = 2, = 4 and = 50. Find the equilibrium quantities demanded of x and z.

Sally consumes two goods, X and Y. Her utility function is given by the expression U = 2XY3. The current market price for X is $20, while the market price for Y is $10. Sally's current income is $500. a. Write the equation for Sally's budget constraint. What is the slope of her budget line? b. Determine the X,Y combination which maximizes Sally's utility, given her budget constraint.

Dan's utility function is U(x,y) =9.5 x2.4y4.9. Dan's income is 129.1 dollars, the price of good X is 4.8 and the price of good Y is 6.3, What is the slope of Dan's income expansion path, dy/dx, on a graph where good X appears on the horizontal axis and good Y appears on the vertical axis. Remember not to enter ratios below, such as 3/4, 2/9 etc. Instead enter the number in decimal form.

Dana's utility function is U(x,y) =3.2 x3.7y7.9. It follows if she has 2.4 units of good X and 1.1 units of good Y, her marginal rate of substitution (of good X in terms of good Y) is equal to ...

Mary has the following utility function: u(x, y) = 3 ln(x) + 2y. Her income is given by I = 10 and the prices originally are p = 1 and py = 2 (b) How much of each good is Mary currently consuming?

Dev likes to consume scones (Good X) and cups of coffee (Good Y). Her utility functionis: U(x,y) = min{x, 2y}That is, her level of utility for any given bundle (x,y) is the lesser of x and 2y.Suppose the price of scones is $3 and the price of coffee is $2. Dev’s weekly budget is$20. Determine her optimal consumption bundle for a week.

Xander has a utility function u(x,y) = xy and an income of M. Assume that the price of x is $4 and the price y is $2. If Xander's income rises from M = 104 to M = 152, what the resulting increase in demand for good x? increases by 6 units increases by 9 units increases by 11 units increases by 14.5 units

Suppose that Sam has a utility function u(x, y)= x+y where x is the amount of good 1 and y is the amount of good 2. The price of good 2 is $20, and the income is $ 90. With the $5 price decrease of good 1 from $10 to $5, then what is the substitution effect and income effect on the demand for good 1?

Laura's preferences over commodities X₁ and x₂ can be represented by U(x₁,x2)=min{3x₁, x₂}. She maximizes her utility subject to her budget constraint. Suppose there is an increase in p1. There are both income and substitution effects of this price change. There is an income effect but not a substitution effect of this price change. There is a substitution effect but not an income effect of this price change. It is unclear whether the consumer will buy more or less x1 as a result of the increase in p1.