1. (18 points) For each of the following situations, i) Find the Marginal Rate of Substitution at the given bundle, and ii) use a graph to indicate the given bundle, and accurately draw the...

3 Major questions, not essay


1. (18 points) For each of the following situations, i) Find the Marginal Rate of Substitution at the given bundle, and ii) use a graph to indicate the given bundle, and accurately draw the indifference curve that goes through that bundle. Be sure to label you graph carefully and accurately. In all cases put the amount of good X on the horizontal axis, and the amount of good Y on the vertical axis. a) The consumers utility function is given by U(X,Y) = X1/2*Y1/2, and the given bundle is X = 4 and Y = 9. i) MRS = __________________________________________________ ii) For this graph, scale each axis up to 36. Do not go above 36 on either axis. Draw your graph in this space: b) The consumers utility function is given by U(X,Y) = MIN(3X, Y), and the given bundle is X = 5 and Y = 6. i) MRS = __________________________________________________ ii) Draw your graph in this space: c) The consumers utility function is given by U(X,Y) = 3X + 2Y and the given bundle is X = 4 and Y = 3. i) MRS = __________________________________________________ ii) Draw your graph in this space: 2) (18 points) For each of the following situations, draw the consumer’s budget constraint and indicate the consumer’s optimal bundle on the budget constraint. Make sure your graph is accurate and clearly labeled. a) U(X,Y) = X1/4Y3/4. The consumer has $24 to spend and the prices of the goods are PX = $2 and PY = $3. Note that the MUX = (1/4)X-3/4Y3/4 and the MUY = (3/4)X1/4Y-1/4. b) U(X,Y) = MIN(5X,Y). The consumer has $24 to spend and the prices of the goods are PX = $3 and PY = $1. c) U(X,Y) = 2X + 3Y. The consumer has $20 to spend and the prices of the goods are PX = $2 and PY = $4. 3. (14 total points) Suppose a consumer has M = $40 to spend. The price of Good X is PX = $2 and the price of Good Y is PY = $5. a) (6 points) Draw the consumer’s budget constraint. Be sure to label your graph accurately, and identify the vertical and horizontal intercepts. (Please put the quantity of Good Y on the Y-axis, and the quantity of Good X on the X-axis). b) (2 points) What is the MRT? MRT = __________________ c) (6 points) Suppose the government wants to limit the amount of Good X that is purchased, so they enact a program where the price of Good X goes up to $4 for any amount of Good X greater than X = 10 units. So PX = $2 if X < 10,="" but="" px="$4" for="" all="" units="" of="" x="" purchased="" where="" x=""> 10. Draw the consumer’s budget constraint. Be sure that your graph is accurate and carefully labeled.