Question 2
A consumer purchases two goods, food (x) and clothing (y). He has the utility function U(X,Y) = XY, where X and Y denote amounts of X and Y consumed. Marginal utilities of X and Y are MUx = y and MUy = x. The consumer’s income is $72 per week and that the price of y is Py = $1 per unit and price of x is Px1 = $9 per unit.
c). Suppose price of x now falls to Px2 = $4.00; income and price of y remain the same. What quantities of X and Y will be consumed after the fall in price of x? Show arithmetically.
d). On the same graph as in part b), show the consumer’s new budget line, new equilibrium point on a new indifference curve. On the diagram label the new quantity consumed of x. What will this quantity be?
e). On the diagram draw the budget line corresponding to the new price of x and tangent to old indifference
curve. (You are trying to separate the income and substitution effects). What will be consumption of x at this
tangency point?
f). What are the price effect, income effect and the substitution effect on the diagram above?
What are their numerical values of these effects?
Question 2 A consumer purchases two goods, food (x) and clothing (y). He has the utility function...
A consumer has the utility function U(X, Y) = (X + 2)(Y + 4). Her income is $100, the price of X is $4, and the price of Y is $5. In order to maximize utility subject to her budget constraint, how many units of X and Y will our consumer choose to purchase? Sketch a budget line – indifference curve diagram illustrating this optimum. Label this optimum A. Suppose the price of X increases to $8, while income and the price...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4) Denote the price of good X by Px, price of good Y by Py and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency...
( Microecomincs Book ) The Answers with Details Q1 Miriam is a college student who spends all of her weekly allowance of S100 (income) on entertainment (X) and health food (Y). P.-S10, Py = $5. and Miriam is originally in equilibrium at point A on the graph below. Ia. Write down the equation for Miriam's weekly budget constraint and label the intersections of the constraint line on the X-axis and on the Y-axis. Health Food (Y) Yi Entertainment (X) Question...
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andy's optimal consumption bundle is X* -6 and Y' = 6. When the prices are Px = 1 and P, = 4, Andy's optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of...
Assume X and Y are economic goods. Plot X on the x axis and Y on the y axis using graph paper. Assume income is $50 and the price of X is $2.50 and the price of Y is $5.00. Draw the original budget line and show a utility maximizing interior equilibrium using an indifference curve. a. Draw a new budget line if the price of X falls to $2.00. Show using indifference curves the substitution and income effects if...
14. Suppose Jack has an income of $12 to buy two goods: sandwiches and sodas. The price of a bottle of soda is $1, and the price of a sandwich is $2. Draw Jack’s budget line (BL1) given his income is $12. (Measure sodas on the X-axis and sandwiches on the Y-axis.) Assume Jack’s utility function is U(x,y)=xy (x is the consumption amount of sodas and y is the consumption amount of sandwiches). Jack’s marginal utility of consuming sodas and...
Exercise 3 For Sandra, coffee and sugar are perfect complements: she wants to consume exactly 2 g of sugar for each cup of coffee. She has S6 to spend on sugar and coffee. One gram of sugar costs 5 cents and one cup of coffee costs 20 cents. Draw a diagram, with sugar on the horizontal axis and cup of coffee on the vertical axis, to answer the following questions. 1. Which bundle will Sandra consume (represented by point A)?...
3) Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3 · XY2. The current market price for X is $10, while the market price for Y is $5. Sally's current income is $500. a. Sketch a set of two indifference curves for Sally in her consumption of X and Y. b. Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. c. Determine the X, Y...
The graph shows Tom’s budget line and indifference curve for good x and y. The price of good x is $40 . If he uses all of his income on good Y , then 20 units of y will be consumed. If all income is spent on good x then 4 units will be consumed. What is the marginal rate of substitution of good y for x at the point where the indifference curve is tangent to the budget line?
UES TION 16 A consumer consumes two commodities, m and n, and has a utility function z = mn. The price of M is Pm- $10 and the price of n is P $40 and the income of the consumer is Y- $180. As you kno optimal bundle there will be a tangency between one of the indifference curves and the budget line. In other words, the slope of the indifference curve and the slope of the budget line will...