Question

Let U(X,Y)= XY You have M = 100 to spend and the price of X is set at Px = 5. Draw the PCC then use it to make a demand curve for Y including the following prices for Y: Py = 1. Py = 5, Py = 10. PCC: Demand Curve:

Answer 1

This question can be solved by first solving the utility function and budget curve for the values quantity of X and Y and then plotting the curves for PCC and Demand

// wer I L a) u = nye P = 5, M=100 Py=1 budget constraint is 5x+y= 100 5 = 100-4 The R x = 100-4 5 . .. uz ays = 100-y]ys = 100y..44 For maximising unitely, we differentiate u and equate A Su 7 100.84 ² - 4 y z S sy 5 5 Equating to gero - r 300 - 4y=0 5 5 y . y no no L&E 100-4 - 100-75 X= 5 =75

When y Py = 5 The budget constraint is- 5x+5y = 100 x+y = 20 U = Xy & x=20-4 = (20-4345 = 20420yt Fellowing the same proudure - maximising Hy he get- | 15 | a) When Py = 10 Then budget constraict 6 - 5x+10y +100 X+ 24 = 20 x=-20-24 U- 2030 =60-24243 = 2073&yt_ . - Wallowing the same prepedure - marrimsing Uy bee get | 25 44 =4.5_

The PCC curve is plotted by taking quantities of X and Y on the x-axis and y-axis respectively and the demand curve is plotted by taking the price of Y on the y-axis and the quantity of Y on the x-axis.

The Pcc graph is a The are points of tangency A45,75) 0(5915) c (5,715) ED 0 10 20 30 40 50 60 70 C 40100X demand care in 4 Py = Py = 59 Py=10 mand cuve are - Qy = 75 Qy = 15 Qy = 7.5 0 . oh q T 1 T 0 10 20 30 40 50 6.70 80 90 100 Quantity